[ { "ref": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles", "label": "SupplementaryAngles", "description": "Supplementary angles add up to 180 degree ", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B" }, "label": "B", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C" }, "label": "C", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D" }, "label": "D", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?L" }, "label": "L", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?A_on_L" }, "label": "A ∈ L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?L", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B_on_L" }, "label": "B ∈ L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?L", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C_on_L" }, "label": "C ∈ L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?L", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?angleABD" }, "label": "∠ABD", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Solution?angleDBC" }, "label": "∠DBC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "value": 180.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?angleABD", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?acos", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?D", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "value": 180.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?SupplementaryAngles/Problem?angleABD", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "By some theorem", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?OppositeLen", "label": "OppositeLen", "description": "Given a triangle △ABC right-angled at ⊾C, the opposite side has length CA = tan(∠ABC) ⋅ BC.", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B" }, "label": "B", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C" }, "label": "C", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC" }, "label": "⊾C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITBasics?rightAngle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "value": 90.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC" }, "label": "BC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB" }, "label": "∠ABC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA" }, "label": "CA", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?tan", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?tan", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "OppositeLen Scroll", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?AngleSum", "label": "AngleSum", "description": "Given a triangle △ABC and two known angles, we can deduce the missing angle by: ∠BCA = 180° - ∠BAC - ∠ABC.", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B" }, "label": "B", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C" }, "label": "C", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA" }, "label": "∠BAC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB" }, "label": "∠ABC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC" }, "label": "∠BCA", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "value": 180.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?acos", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "value": 180.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "By sum of interior angles = 180° in triangles", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?Pythagoras", "label": "Pythagoras", "description": "Given a ABC right-angled at C and lengths of both legs, we can compute the length of the hypotenuse via Pythagora's theorem", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B" }, "label": "B", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C" }, "label": "C", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC" }, "label": "⊾C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITBasics?rightAngle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "value": 90.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceAC" }, "label": "AC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceBC" }, "label": "BC", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Solution?deducedHypotenuse" }, "label": "BA", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceAC", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceAC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceBC", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceBC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceAC", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceAC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceBC", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Pythagoras/Problem?distanceBC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "By Pythagora's theorem", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?CylinderVolumeScroll", "label": "CylinderVolumeScroll", "description": "This scroll caclculates the volume of a cylinder with top ○c, base ○C, height [MS] and intersection points M and S. The formula is V = [MS] ⋅ A(○C) . ", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S" }, "label": "S", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M" }, "label": "M", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base" }, "label": "○C", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H" }, "label": "SM", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height" }, "label": "[MS]", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase" }, "label": "A(○C)", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?areaCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?orthoBaseH" }, "label": " ○C⊥SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S_on_H" }, "label": "S∈SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?I_on_H" }, "label": "M∈SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?I_on_C" }, "label": "M∈○C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top" }, "label": "○c", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?orthoTopH" }, "label": " ○c⊥SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?S_on_Top" }, "label": "S∈○c", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CylinderVolumeScroll/Problem?proofOfEqualSize" }, "label": "○C=○c", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?equalityCircles", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CylinderVolumeScroll/Solution?deduceVolume" }, "label": "V:○C○c ", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCylinder?cylinderVolume", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCylinder?mkCylinder", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CylinderVolumeScroll/Problem?proofOfEqualSize", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?proofParallelCircles", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?orthoBaseH", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?orthoTopH", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "CylinderVolume Scroll", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll", "label": "CircleLineAngleToAngle", "description": "CircleLineAngle don't work as normal angles, therefore this scrolls converts a CircleLineAngle ∠○CL to a normal angle ∠PBA, if it is 90°.", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?C" }, "label": "○C", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?L" }, "label": "L", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?orthogonalCircleLine" }, "label": " ○C⊥L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?planeLineAngle" }, "label": "∠○CL", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?angleCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B" }, "label": "B", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P" }, "label": "P", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A_on_L" }, "label": "A∈L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?L", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B_on_L" }, "label": " B∈L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?L", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B_on_C" }, "label": " B∈○C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P_on_C" }, "label": " P∈○C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Solution?deduceAngle" }, "label": "∠PBA", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?planeLineAngle", "kind": "OMS" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?acos", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll/Problem?planeLineAngle", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "CastAngle", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?Midpoint", "label": "MidPoint", "description": "Our MidPoint scroll that given two points P and Q computes the midpoint of the line PQ.", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P" }, "label": "P", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?Q" }, "label": "Q", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Solution?midpoint" }, "label": "Mid[PQ]", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 0.5, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?Q", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 0.5, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?Q", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 0.5, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?Q", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "kind": "general" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?CircleScroll", "label": "CircleScroll", "description": "Calculating a circle defined by the middle M, an edge point A and a point on the circle plane B. ", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M" }, "label": "M", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B" }, "label": "B", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?deduceC" }, "label": "○M", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circle3D", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?pointNormalPlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 1.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 1.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 1.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?deduceR" }, "label": "r○M", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?deduceC", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "deduce Radius", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?deduceR2" }, "label": "AM", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "deduce Radius2", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?midOnCircle" }, "label": "M∈○M", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?deduceC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?midAlwaysOnCircle", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circle3D", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?pointNormalPlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 1.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 1.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 1.0, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?B", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Product", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" } ], "kind": "OMA" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?M", "kind": "OMS" } ], "kind": "OMA" }, { "value": "trivial", "kind": "OMLIT<String>" } ], "kind": "OMA" } ], "kind": "OMA" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?edgeOnCircle" }, "label": "A∈○M", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Solution?deduceC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?WBouncingScroll", "label": "WBouncingScroll", "description": "Bouncing 2D", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?WBouncingScroll/Problem?position" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?WBouncingScroll/Problem?velocity" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?WBouncingScroll/Problem?g_base" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?WBouncingScroll/Problem?bounce" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?WBouncingScroll/Problem?walls" }, "kind": "general" } ], "acquiredFacts": [] }, { "ref": "http://mathhub.info/FrameIT/frameworld?W3DBouncingScroll", "label": "W3DBouncingScroll", "description": "Bouncing 3D", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?W3DBouncingScroll/Problem?position" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?W3DBouncingScroll/Problem?velocity" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?W3DBouncingScroll/Problem?g_base" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?W3DBouncingScroll/Problem?bounce" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?W3DBouncingScroll/Problem?wallsr" }, "kind": "general" } ], "acquiredFacts": [] }, { "ref": "http://mathhub.info/FrameIT/frameworld?T3DBouncingScroll", "label": "T3DBouncingScroll", "description": "Bouncing 3D with Triangles!", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?T3DBouncingScroll/Problem?position" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?T3DBouncingScroll/Problem?velocity" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?T3DBouncingScroll/Problem?g_base" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?T3DBouncingScroll/Problem?bounce" }, "kind": "general" },{ "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?T3DBouncingScroll/Problem?wallsr" }, "kind": "general" } ], "acquiredFacts": [] }, { "ref": "http://mathhub.info/FrameIT/frameworld?RiverScroll", "label": "RiverScroll", "description": "River.", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?RiverScroll/Problem?A" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?RiverScroll/Problem?B" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?RiverScroll/Problem?C" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?RiverScroll/Problem?D" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?RiverScroll/Problem?G" }, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?RiverScroll/Problem?angleA" }, "kind": "general" } ], "acquiredFacts": [] }, { "ref": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll", "label": "CircleLineAngleScroll", "description": " Caclculates the angle between the plane of ○C and the line L ", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C" }, "label": "○C", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L" }, "label": "L", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?A" }, "label": "A", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?A_on_L" }, "label": " A∈L", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?A_on_C" }, "label": " A∈○C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?A", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Solution?deduceAngle" }, "label": "∠○CL", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?angleCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?asin", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3183098861837907, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 180.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?asin", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3183098861837907, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 180.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?asin", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?C", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?targetpoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?basepoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll/Problem?L", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3183098861837907, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 180.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "PlaneAngleScroll Scroll", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll", "label": "CircleAreaScroll", "description": " This scroll is calculating the area of the circle ○C via the formula A = r⋅ r⋅ pi", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?cir" }, "label": "○C", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?radiusC" }, "label": "r", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?cir", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Solution?deduceArea" }, "label": "A(○C)", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?areaCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?cir", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?radiusC", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?radiusC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?cir", "kind": "OMS" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?radiusC", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?CircleAreaScroll/Problem?radiusC", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "CircleArea Scroll", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?ConeVolumeScroll", "label": "ConeVolumeScroll", "description": "This scroll caclculates the volume of a cone with apex S and base ○C with area A(○C) and the height [MS]. The formula is V = [MS] ⋅ A(○C) / 3 . ", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S" }, "label": "S", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M" }, "label": "M", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base" }, "label": "○C", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H" }, "label": "SM", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height" }, "label": "[MS]", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase" }, "label": "A(○C)", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?areaCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?orthoBaseH" }, "label": " ○C⊥SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S_on_H" }, "label": "S∈SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?I_on_H" }, "label": "M∈SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?I_on_C" }, "label": "M∈○C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeVolumeScroll/Solution?deduceVolume" }, "label": "V ○C ", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCone?volumeCone", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCone?circleConeOf", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3333333333333333, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeBase", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeBase", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeBase", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3333333333333333, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3333333333333333, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "ConeVolume Scroll", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] }, { "ref": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll", "label": "TruncatedConeVolumeScroll", "description": "This scroll caclculates the volume of a truncated cone with top ○c, base ○C and height [MS]. The formula is: V = [MS] ⋅ ( A(○C) + √(A(○c) ⋅ A(○C) ) + A(○c)) / 3 . ", "requiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S" }, "label": "S", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M" }, "label": "M", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base" }, "label": "○C", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H" }, "label": "SM", "tp": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height" }, "label": "[MS]", "lhs": { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase" }, "label": "A(○C)", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?areaCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?orthoBaseH" }, "label": " ○C⊥SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S_on_H" }, "label": "S∈SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?I_on_H" }, "label": "M∈SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?I_on_C" }, "label": "M∈○C", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?M", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top" }, "label": "○c", "tp": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D", "kind": "OMS" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?orthoTopH" }, "label": " ○c⊥SM", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?S_on_Top" }, "label": "S∈○c", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?S", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?areaTop" }, "label": "A(○c)", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?areaCircle", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": null, "proof": null, "kind": "veq" }, { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?proofOfUnEqualSize" }, "label": "○C≠○c", "tp": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?ded", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?unequalityCircles", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, "df": null, "kind": "general" } ], "acquiredFacts": [ { "ref": { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Solution?deduceVolume" }, "label": "V:○C○c ", "lhs": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCone?truncatedConeVolume", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCone?mkTruncatedCone", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?proofOfUnEqualSize", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?proofParallelCircles", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?H", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?orthoBaseH", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?orthoTopH", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, "valueTp": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "value": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?areaTop", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?areaTop", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3333333333333333, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, "proof": { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?Logic?eq", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "value": 0.3333333333333333, "kind": "OMLIT<Double>" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleMidPoint", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeBase", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeBase", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeBase", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?inv_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projr", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/core/geometry?Planes?planeNormal", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circlePlane", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 4.626e-12, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?base", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_pow", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeProblem?top", "kind": "OMS" } ], "kind": "OMA" }, { "value": 2.0, "kind": "OMLIT<Double>" } ], "kind": "OMA" }, { "value": 3.141592653589793, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?sqrt", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit", "kind": "OMS" }, "arguments": [ { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?areaBase", "kind": "OMS" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?areaTop", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll/Problem?areaTop", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "applicant": { "uri": "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Projl", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?ConeProblem?height", "kind": "OMS" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": 0.3333333333333333, "kind": "OMLIT<Double>" } ], "kind": "OMA" } ], "kind": "OMA" }, { "value": "TruncatedConeVolume Scroll", "kind": "OMLIT<String>" } ], "kind": "OMA" }, "kind": "veq" } ] } ]