scrolls.json

[
    {
        "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": {
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                    "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"
                },
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                    "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": {
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                        "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?times_real_lit",
                        "kind": "OMS"
                    },
                    "arguments": [
                        {
                            "applicant": {
                                "uri": "http://mathhub.info/MitM/Foundation?Trigonometry?tan",
                                "kind": "OMS"
                            },
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                                {
                                    "xml": "no raw OMDoc XML here for performance reasons",
                                    "kind": "RAW"
                                }
                            ],
                            "kind": "OMA"
                        },
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                            "kind": "RAW"
                        }
                    ],
                    "kind": "OMA"
                },
                "proof": {
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                        "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"
                                                        },
                                                        {
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                                                            "kind": "RAW"
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                                            ],
                                            "kind": "OMA"
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                                    ],
                                    "kind": "OMA"
                                },
                                {
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                                        "kind": "OMS"
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                                            "kind": "RAW"
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                                    ],
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                            ],
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                            "string": "OppositeLen Scroll",
                            "kind": "OMSTR"
                        }
                    ],
                    "kind": "OMA"
                },
                "kind": "veq"
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        ]
    },
    {
        "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",
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            {
                "ref": {
                    "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B"
                },
                "label": "B",
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                    "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point",
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                "df": null,
                "kind": "general"
            },
            {
                "ref": {
                    "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C"
                },
                "label": "C",
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                    "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",
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                    ],
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                },
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                "proof": null,
                "kind": "veq"
            },
            {
                "ref": {
                    "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB"
                },
                "label": "∠ABC",
                "lhs": {
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                        "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",
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                    },
                    "arguments": [
                        {
                            "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?B",
                            "kind": "OMS"
                        },
                        {
                            "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?C",
                            "kind": "OMS"
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                            "uri": "http://mathhub.info/FrameIT/frameworld?TriangleProblem?A",
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                    "kind": "OMA"
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                                "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?plus_real_lit",
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                                    "applicant": {
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                            "applicant": {
                                "uri": "http://mathhub.info/MitM/Foundation?Logic?eq",
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                                    "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit",
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                                                                            "kind": "OMA"
                                                                        },
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                                                                                "kind": "OMS"
                                                                            },
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