Skip to content
Snippets Groups Projects
Select Git revision
  • 0a5139c2d76888ee4d0372d735a9605e12b25b9e
  • master default
  • JS-based-scroll-rendering
  • Paul_Marius_Level
  • Paul_Marius_2
  • Paul_Marius
  • Andi_Mark
  • be-UnityWebView
  • gitignoreFrameitServer
  • ZimmerBSc
  • Bugfix_StageLoading
  • stages
  • MAZIFAU_Experimental
  • tsc/coneworld
  • tsc/fact-interaction
  • marcel
  • MaZiFAU_TopSort
  • mergeHelper
  • zwischenSpeichern
  • tempAndrToMaster
  • SebBranch
  • 3.0
  • v2.1
  • v2.0
  • v1.0
25 results

scrolls.json

Blame
  • scrolls.json 77.22 KiB
    [
        {
            "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/core/arithmetics?RealArithmetics?multiplication",
                                    "kind": "OMS"
                                },
                                "arguments": [
                                    {
                                        "float": 0.5,
                                        "kind": "OMF"
                                    },
                                    {
                                        "applicant": {
                                            "uri": "http://mathhub.info/MitM/core/arithmetics?RealArithmetics?addition",
                                            "kind": "OMS"
                                        },
                                        "arguments": [
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?xofpoint",
                                                    "kind": "OMS"
                                                },
                                                "arguments": [
                                                    {
                                                        "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P",
                                                        "kind": "OMS"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            },
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?xofpoint",
                                                    "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/core/arithmetics?RealArithmetics?multiplication",
                                    "kind": "OMS"
                                },
                                "arguments": [
                                    {
                                        "float": 0.5,
                                        "kind": "OMF"
                                    },
                                    {
                                        "applicant": {
                                            "uri": "http://mathhub.info/MitM/core/arithmetics?RealArithmetics?addition",
                                            "kind": "OMS"
                                        },
                                        "arguments": [
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?yofpoint",
                                                    "kind": "OMS"
                                                },
                                                "arguments": [
                                                    {
                                                        "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P",
                                                        "kind": "OMS"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            },
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?yofpoint",
                                                    "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/core/arithmetics?RealArithmetics?multiplication",
                                    "kind": "OMS"
                                },
                                "arguments": [
                                    {
                                        "float": 0.5,
                                        "kind": "OMF"
                                    },
                                    {
                                        "applicant": {
                                            "uri": "http://mathhub.info/MitM/core/arithmetics?RealArithmetics?addition",
                                            "kind": "OMS"
                                        },
                                        "arguments": [
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?zofpoint",
                                                    "kind": "OMS"
                                                },
                                                "arguments": [
                                                    {
                                                        "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?P",
                                                        "kind": "OMS"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            },
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?zofpoint",
                                                    "kind": "OMS"
                                                },
                                                "arguments": [
                                                    {
                                                        "uri": "http://mathhub.info/FrameIT/frameworld?Midpoint/Problem?Q",
                                                        "kind": "OMS"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            }
                                        ],
                                        "kind": "OMA"
                                    }
                                ],
                                "kind": "OMA"
                            }
                        ],
                        "kind": "OMA"
                    },
                    "kind": "general"
                }
            ]
        },
        {
            "ref": "http://mathhub.info/FrameIT/frameworld?OppositeLen",
            "label": "OppositeLen",
            "description": "Given a triangle △ABC right-angled at ⊾C, the opposide 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/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"
                                    },
                                    {
                                        "float": 90.0,
                                        "kind": "OMF"
                                    }
                                ],
                                "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": [
                                    {
                                        "xml": "no raw OMDoc XML here for performance reasons",
                                        "kind": "RAW"
                                    }
                                ],
                                "kind": "OMA"
                            },
                            {
                                "xml": "no raw OMDoc XML here for performance reasons",
                                "kind": "RAW"
                            }
                        ],
                        "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?DescriptionOperator?that",
                                            "kind": "OMS"
                                        },
                                        "arguments": [
                                            {
                                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                "kind": "OMS"
                                            },
                                            {
                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                "kind": "RAW"
                                            },
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/Foundation?Logic?ImplicitProof",
                                                    "kind": "OMS"
                                                },
                                                "arguments": [
                                                    {
                                                        "applicant": {
                                                            "uri": "http://mathhub.info/MitM/Foundation?Logic?exists",
                                                            "kind": "OMS"
                                                        },
                                                        "arguments": [
                                                            {
                                                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                "kind": "OMS"
                                                            },
                                                            {
                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                "kind": "RAW"
                                                            }
                                                        ],
                                                        "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": [
                                                    {
                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                        "kind": "RAW"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            },
                                            {
                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                "kind": "RAW"
                                            }
                                        ],
                                        "kind": "OMA"
                                    }
                                ],
                                "kind": "OMA"
                            },
                            {
                                "string": "OppositeLen Scroll",
                                "kind": "OMSTR"
                            }
                        ],
                        "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": [
                                    {
                                        "float": 180.0,
                                        "kind": "OMF"
                                    },
                                    {
                                        "applicant": {
                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                            "kind": "OMS"
                                        },
                                        "arguments": [
                                            {
                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                "kind": "RAW"
                                            }
                                        ],
                                        "kind": "OMA"
                                    }
                                ],
                                "kind": "OMA"
                            },
                            {
                                "applicant": {
                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                    "kind": "OMS"
                                },
                                "arguments": [
                                    {
                                        "xml": "no raw OMDoc XML here for performance reasons",
                                        "kind": "RAW"
                                    }
                                ],
                                "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": [
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    },
                                                                                    {
                                                                                        "applicant": {
                                                                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                                                            "kind": "OMS"
                                                                                        },
                                                                                        "arguments": [
                                                                                            {
                                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                "kind": "RAW"
                                                                                            }
                                                                                        ],
                                                                                        "kind": "OMA"
                                                                                    }
                                                                                ],
                                                                                "kind": "OMA"
                                                                            },
                                                                            {
                                                                                "applicant": {
                                                                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit",
                                                                                    "kind": "OMS"
                                                                                },
                                                                                "arguments": [
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    },
                                                                                    {
                                                                                        "applicant": {
                                                                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                                                            "kind": "OMS"
                                                                                        },
                                                                                        "arguments": [
                                                                                            {
                                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                "kind": "RAW"
                                                                                            }
                                                                                        ],
                                                                                        "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": [
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    },
                                                                                    {
                                                                                        "applicant": {
                                                                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                                                            "kind": "OMS"
                                                                                        },
                                                                                        "arguments": [
                                                                                            {
                                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                "kind": "RAW"
                                                                                            }
                                                                                        ],
                                                                                        "kind": "OMA"
                                                                                    }
                                                                                ],
                                                                                "kind": "OMA"
                                                                            },
                                                                            {
                                                                                "applicant": {
                                                                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit",
                                                                                    "kind": "OMS"
                                                                                },
                                                                                "arguments": [
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    },
                                                                                    {
                                                                                        "applicant": {
                                                                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                                                            "kind": "OMS"
                                                                                        },
                                                                                        "arguments": [
                                                                                            {
                                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                "kind": "RAW"
                                                                                            }
                                                                                        ],
                                                                                        "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": [
                                                                            {
                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                "kind": "RAW"
                                                                            },
                                                                            {
                                                                                "applicant": {
                                                                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                                                    "kind": "OMS"
                                                                                },
                                                                                "arguments": [
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    }
                                                                                ],
                                                                                "kind": "OMA"
                                                                            }
                                                                        ],
                                                                        "kind": "OMA"
                                                                    },
                                                                    {
                                                                        "applicant": {
                                                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit",
                                                                            "kind": "OMS"
                                                                        },
                                                                        "arguments": [
                                                                            {
                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                "kind": "RAW"
                                                                            },
                                                                            {
                                                                                "applicant": {
                                                                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                                                    "kind": "OMS"
                                                                                },
                                                                                "arguments": [
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    }
                                                                                ],
                                                                                "kind": "OMA"
                                                                            }
                                                                        ],
                                                                        "kind": "OMA"
                                                                    }
                                                                ],
                                                                "kind": "OMA"
                                                            }
                                                        ],
                                                        "kind": "OMA"
                                                    },
                                                    {
                                                        "applicant": {
                                                            "uri": "http://mathhub.info/MitM/core/arithmetics?RealArithmetics?inverse",
                                                            "kind": "OMS"
                                                        },
                                                        "arguments": [
                                                            {
                                                                "applicant": {
                                                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit",
                                                                    "kind": "OMS"
                                                                },
                                                                "arguments": [
                                                                    {
                                                                        "applicant": {
                                                                            "uri": "http://mathhub.info/MitM/Foundation?DescriptionOperator?that",
                                                                            "kind": "OMS"
                                                                        },
                                                                        "arguments": [
                                                                            {
                                                                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                "kind": "OMS"
                                                                            },
                                                                            {
                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                "kind": "RAW"
                                                                            },
                                                                            {
                                                                                "applicant": {
                                                                                    "uri": "http://mathhub.info/MitM/Foundation?Logic?ImplicitProof",
                                                                                    "kind": "OMS"
                                                                                },
                                                                                "arguments": [
                                                                                    {
                                                                                        "applicant": {
                                                                                            "uri": "http://mathhub.info/MitM/Foundation?Logic?exists",
                                                                                            "kind": "OMS"
                                                                                        },
                                                                                        "arguments": [
                                                                                            {
                                                                                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                                "kind": "OMS"
                                                                                            },
                                                                                            {
                                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                "kind": "RAW"
                                                                                            }
                                                                                        ],
                                                                                        "kind": "OMA"
                                                                                    }
                                                                                ],
                                                                                "kind": "OMA"
                                                                            }
                                                                        ],
                                                                        "kind": "OMA"
                                                                    },
                                                                    {
                                                                        "applicant": {
                                                                            "uri": "http://mathhub.info/MitM/Foundation?DescriptionOperator?that",
                                                                            "kind": "OMS"
                                                                        },
                                                                        "arguments": [
                                                                            {
                                                                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                "kind": "OMS"
                                                                            },
                                                                            {
                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                "kind": "RAW"
                                                                            },
                                                                            {
                                                                                "applicant": {
                                                                                    "uri": "http://mathhub.info/MitM/Foundation?Logic?ImplicitProof",
                                                                                    "kind": "OMS"
                                                                                },
                                                                                "arguments": [
                                                                                    {
                                                                                        "applicant": {
                                                                                            "uri": "http://mathhub.info/MitM/Foundation?Logic?exists",
                                                                                            "kind": "OMS"
                                                                                        },
                                                                                        "arguments": [
                                                                                            {
                                                                                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                                "kind": "OMS"
                                                                                            },
                                                                                            {
                                                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                "kind": "RAW"
                                                                                            }
                                                                                        ],
                                                                                        "kind": "OMA"
                                                                                    }
                                                                                ],
                                                                                "kind": "OMA"
                                                                            }
                                                                        ],
                                                                        "kind": "OMA"
                                                                    }
                                                                ],
                                                                "kind": "OMA"
                                                            },
                                                            {
                                                                "applicant": {
                                                                    "uri": "http://mathhub.info/MitM/Foundation?Logic?ImplicitProof",
                                                                    "kind": "OMS"
                                                                },
                                                                "arguments": [
                                                                    {
                                                                        "applicant": {
                                                                            "uri": "http://mathhub.info/MitM/Foundation?Logic?not",
                                                                            "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?DescriptionOperator?that",
                                                                                                    "kind": "OMS"
                                                                                                },
                                                                                                "arguments": [
                                                                                                    {
                                                                                                        "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                                        "kind": "OMS"
                                                                                                    },
                                                                                                    {
                                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                        "kind": "RAW"
                                                                                                    },
                                                                                                    {
                                                                                                        "applicant": {
                                                                                                            "uri": "http://mathhub.info/MitM/Foundation?Logic?ImplicitProof",
                                                                                                            "kind": "OMS"
                                                                                                        },
                                                                                                        "arguments": [
                                                                                                            {
                                                                                                                "applicant": {
                                                                                                                    "uri": "http://mathhub.info/MitM/Foundation?Logic?exists",
                                                                                                                    "kind": "OMS"
                                                                                                                },
                                                                                                                "arguments": [
                                                                                                                    {
                                                                                                                        "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                                                        "kind": "OMS"
                                                                                                                    },
                                                                                                                    {
                                                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                                        "kind": "RAW"
                                                                                                                    }
                                                                                                                ],
                                                                                                                "kind": "OMA"
                                                                                                            }
                                                                                                        ],
                                                                                                        "kind": "OMA"
                                                                                                    }
                                                                                                ],
                                                                                                "kind": "OMA"
                                                                                            },
                                                                                            {
                                                                                                "applicant": {
                                                                                                    "uri": "http://mathhub.info/MitM/Foundation?DescriptionOperator?that",
                                                                                                    "kind": "OMS"
                                                                                                },
                                                                                                "arguments": [
                                                                                                    {
                                                                                                        "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                                        "kind": "OMS"
                                                                                                    },
                                                                                                    {
                                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                        "kind": "RAW"
                                                                                                    },
                                                                                                    {
                                                                                                        "applicant": {
                                                                                                            "uri": "http://mathhub.info/MitM/Foundation?Logic?ImplicitProof",
                                                                                                            "kind": "OMS"
                                                                                                        },
                                                                                                        "arguments": [
                                                                                                            {
                                                                                                                "applicant": {
                                                                                                                    "uri": "http://mathhub.info/MitM/Foundation?Logic?exists",
                                                                                                                    "kind": "OMS"
                                                                                                                },
                                                                                                                "arguments": [
                                                                                                                    {
                                                                                                                        "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
                                                                                                                        "kind": "OMS"
                                                                                                                    },
                                                                                                                    {
                                                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                                                        "kind": "RAW"
                                                                                                                    }
                                                                                                                ],
                                                                                                                "kind": "OMA"
                                                                                                            }
                                                                                                        ],
                                                                                                        "kind": "OMA"
                                                                                                    }
                                                                                                ],
                                                                                                "kind": "OMA"
                                                                                            }
                                                                                        ],
                                                                                        "kind": "OMA"
                                                                                    },
                                                                                    {
                                                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                                                        "kind": "RAW"
                                                                                    }
                                                                                ],
                                                                                "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": [
                                                    {
                                                        "float": 180.0,
                                                        "kind": "OMF"
                                                    },
                                                    {
                                                        "applicant": {
                                                            "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                            "kind": "OMS"
                                                        },
                                                        "arguments": [
                                                            {
                                                                "xml": "no raw OMDoc XML here for performance reasons",
                                                                "kind": "RAW"
                                                            }
                                                        ],
                                                        "kind": "OMA"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            },
                                            {
                                                "applicant": {
                                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?minus_real_lit",
                                                    "kind": "OMS"
                                                },
                                                "arguments": [
                                                    {
                                                        "xml": "no raw OMDoc XML here for performance reasons",
                                                        "kind": "RAW"
                                                    }
                                                ],
                                                "kind": "OMA"
                                            }
                                        ],
                                        "kind": "OMA"
                                    }
                                ],
                                "kind": "OMA"
                            },
                            {
                                "string": "By sum of interior angles = 180° in triangles",
                                "kind": "OMSTR"
                            }
                        ],
                        "kind": "OMA"
                    },
                    "kind": "veq"
                }
            ]
        }
    ]