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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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        },
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          "kind": "lemma",
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          "name": "hasEval_pair",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/AdicFormalGroupLog.lean#L590"
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "theorem",
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      "declarations": [
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          "kind": "instance",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "def",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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        {
          "kind": "instance",
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          "kind": "lemma",
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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "abbrev",
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          "kind": "def",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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        {
          "kind": "lemma",
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        {
          "kind": "def",
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          "name": "map",
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        {
          "kind": "lemma",
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          "name": "map_mk",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L240"
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          "kind": "lemma",
          "line": 245,
          "name": "map_id",
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        {
          "kind": "lemma",
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          "name": "map_comp",
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          "kind": "lemma",
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          "name": "map_unit",
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          "kind": "def",
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          "name": "congr",
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        },
        {
          "kind": "lemma",
          "line": 267,
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          "kind": "lemma",
          "line": 276,
          "name": "bijective_map",
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          "kind": "def",
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          "name": "piEquiv",
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        {
          "kind": "lemma",
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          "name": "piEquiv_mk",
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        {
          "kind": "lemma",
          "line": 305,
          "name": "Ideal.comap_ne_bot_of_comap_comap_ne_bot",
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        },
        {
          "kind": "lemma",
          "line": 316,
          "name": "linearIndependent_of_diagonal",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L316"
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        {
          "kind": "theorem",
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          "name": "Matrix.det_blockDiagonal'",
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          "kind": "theorem",
          "line": 355,
          "name": "LinearMap.det_pi'",
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        {
          "kind": "lemma",
          "line": 383,
          "name": "Valuation.map_natCast_le_one",
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        {
          "kind": "lemma",
          "line": 392,
          "name": "Valuation.eq_one_of_mul_eq_one",
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        },
        {
          "kind": "lemma",
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        },
        {
          "kind": "lemma",
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          "name": "Valuation.le_one_of_root_monic",
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        },
        {
          "kind": "lemma",
          "line": 442,
          "name": "IsDedekindDomain.HeightOneSpectrum.finite_setOf_valuation_ne_one",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L442"
        },
        {
          "kind": "lemma",
          "line": 452,
          "name": "Set.integer_mono",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L452"
        },
        {
          "kind": "lemma",
          "line": 456,
          "name": "Set.unit_mono",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L456"
        },
        {
          "kind": "lemma",
          "line": 461,
          "name": "IsDedekindDomain.HeightOneSpectrum.le_count_iff_le",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L461"
        },
        {
          "kind": "lemma",
          "line": 469,
          "name": "IsDedekindDomain.HeightOneSpectrum.le_count_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L469"
        },
        {
          "kind": "lemma",
          "line": 477,
          "name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L477"
        },
        {
          "kind": "lemma",
          "line": 484,
          "name": "IsDedekindDomain.HeightOneSpectrum.dvd_toAdd_valuationOfNeZero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L484"
        },
        {
          "kind": "lemma",
          "line": 495,
          "name": "IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroMod_mk_eq_one_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L495"
        },
        {
          "kind": "lemma",
          "line": 507,
          "name": "IsDedekindDomain.HeightOneSpectrum.valuation_algebraMap_eq_one_of_pow_eq_span",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L507"
        },
        {
          "kind": "lemma",
          "line": 518,
          "name": "IsDedekindDomain.HeightOneSpectrum.exp_neg_one_le_valuation_algebraMap",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L518"
        },
        {
          "kind": "lemma",
          "line": 531,
          "name": "IsDedekindDomain.HeightOneSpectrum.notMem_pow_two_of_squarefree",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L531"
        },
        {
          "kind": "def",
          "line": 545,
          "name": "IsDedekindDomain.HeightOneSpectrum.primesAbove",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L545"
        },
        {
          "kind": "lemma",
          "line": 553,
          "name": "IsDedekindDomain.HeightOneSpectrum.primesAbove_mono",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L553"
        },
        {
          "kind": "lemma",
          "line": 560,
          "name": "IsDedekindDomain.HeightOneSpectrum.primesAbove_empty",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L560"
        },
        {
          "kind": "def",
          "line": 566,
          "name": "IsDedekindDomain.HeightOneSpectrum.below",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L566"
        },
        {
          "kind": "lemma",
          "line": 573,
          "name": "IsDedekindDomain.HeightOneSpectrum.below_asIdeal",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L573"
        },
        {
          "kind": "instance",
          "line": 578,
          "name": "IsDedekindDomain.HeightOneSpectrum.instLiesOverBelow",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L578"
        },
        {
          "kind": "lemma",
          "line": 583,
          "name": "IsDedekindDomain.HeightOneSpectrum.mem_primesAbove_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L583"
        },
        {
          "kind": "lemma",
          "line": 591,
          "name": "IsDedekindDomain.HeightOneSpectrum.primesAbove_finite",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L591"
        },
        {
          "kind": "def",
          "line": 605,
          "name": "IsDedekindDomain.selmerGroupAbove",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L605"
        },
        {
          "kind": "lemma",
          "line": 610,
          "name": "IsDedekindDomain.mem_selmerGroupAbove_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L610"
        },
        {
          "kind": "lemma",
          "line": 618,
          "name": "IsDedekindDomain.selmerGroupAbove_empty",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L618"
        },
        {
          "kind": "lemma",
          "line": 629,
          "name": "asIdeal_maximalIdeal",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L629"
        },
        {
          "kind": "lemma",
          "line": 634,
          "name": "_root_.IsDedekindDomain.HeightOneSpectrum.eq_maximalIdeal",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L634"
        },
        {
          "kind": "def",
          "line": 646,
          "name": "comapOfNeBot",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L646"
        },
        {
          "kind": "lemma",
          "line": 655,
          "name": "comapOfNeBot_asIdeal",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L655"
        },
        {
          "kind": "theorem",
          "line": 666,
          "name": "exists_valuationOfNeZero_map_eq",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L666"
        },
        {
          "kind": "theorem",
          "line": 690,
          "name": "dvd_toAdd_valuationOfNeZero_map",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L690"
        },
        {
          "kind": "theorem",
          "line": 701,
          "name": "comap_maximalIdeal_adicCompletionIntegers",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L701"
        },
        {
          "kind": "lemma",
          "line": 722,
          "name": "resultant_C_sub_X",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L722"
        },
        {
          "kind": "lemma",
          "line": 730,
          "name": "Monic.resultant_one_right",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L730"
        },
        {
          "kind": "lemma",
          "line": 738,
          "name": "Monic.resultant_congr_right",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L738"
        },
        {
          "kind": "lemma",
          "line": 744,
          "name": "succ_mul_div_two",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L744"
        },
        {
          "kind": "lemma",
          "line": 752,
          "name": "resultant_X_sub_C_add_mul_derivative",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L752"
        },
        {
          "kind": "lemma",
          "line": 759,
          "name": "resultant_add_mul_derivative",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L759"
        },
        {
          "kind": "theorem",
          "line": 775,
          "name": "discr_X_sub_C_mul",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L775"
        },
        {
          "kind": "lemma",
          "line": 813,
          "name": "mem_degreeLT_natDegree_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L813"
        },
        {
          "kind": "theorem",
          "line": 819,
          "name": "eval_pos_of_monic_of_irreducible_of_natDegree_eq_two",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L819"
        },
        {
          "kind": "lemma",
          "line": 829,
          "name": "exists_eq_C_mul_X_sub_C_of_natDegree_le_one",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L829"
        },
        {
          "kind": "lemma",
          "line": 841,
          "name": "modByMonic_mem_degreeLT",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L841"
        },
        {
          "kind": "lemma",
          "line": 845,
          "name": "divByMonic_mem_degreeLT",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L845"
        },
        {
          "kind": "lemma",
          "line": 856,
          "name": "eq_zero_of_monic_dvd_of_degree_lt",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L856"
        },
        {
          "kind": "lemma",
          "line": 860,
          "name": "Monic.divMod_mul_add",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L860"
        },
        {
          "kind": "lemma",
          "line": 866,
          "name": "Monic.divByMonic_mul_add",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L866"
        },
        {
          "kind": "lemma",
          "line": 870,
          "name": "Monic.modByMonic_mul_add",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L870"
        },
        {
          "kind": "def",
          "line": 905,
          "name": "mulModByMonic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L905"
        },
        {
          "kind": "lemma",
          "line": 912,
          "name": "mulModByMonic_apply_coe",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L912"
        },
        {
          "kind": "def",
          "line": 919,
          "name": "sylvesterEquivOne",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L919"
        },
        {
          "kind": "lemma",
          "line": 944,
          "name": "coe_sylvesterEquivOne",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L944"
        },
        {
          "kind": "lemma",
          "line": 949,
          "name": "coe_sylvesterEquivOne_symm",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L949"
        },
        {
          "kind": "def",
          "line": 965,
          "name": "sylvesterBlock",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L965"
        },
        {
          "kind": "lemma",
          "line": 970,
          "name": "coe_sylvesterBlock_apply_fst",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L970"
        },
        {
          "kind": "lemma",
          "line": 977,
          "name": "coe_sylvesterBlock_apply_snd",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L977"
        },
        {
          "kind": "lemma",
          "line": 985,
          "name": "det_sylvesterBlock",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L985"
        },
        {
          "kind": "theorem",
          "line": 1020,
          "name": "Monic.irreducible_map_fraction_map_of_irreducible_map",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1020"
        },
        {
          "kind": "lemma",
          "line": 1036,
          "name": "mk_modByMonic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1036"
        },
        {
          "kind": "lemma",
          "line": 1039,
          "name": "exists_degree_lt_mk_eq",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1039"
        },
        {
          "kind": "lemma",
          "line": 1044,
          "name": "mk_eq_mk_iff_of_degree_lt",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1044"
        },
        {
          "kind": "def",
          "line": 1052,
          "name": "degreeLTEquiv",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1052"
        },
        {
          "kind": "lemma",
          "line": 1067,
          "name": "degreeLTEquiv_apply",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1067"
        },
        {
          "kind": "theorem",
          "line": 1074,
          "name": "nonempty_algEquiv_complex",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1074"
        },
        {
          "kind": "lemma",
          "line": 1085,
          "name": "norm_mk_eq_det_mulModByMonic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1085"
        },
        {
          "kind": "lemma",
          "line": 1098,
          "name": "norm_mk_eq_resultant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1098"
        },
        {
          "kind": "theorem",
          "line": 1119,
          "name": "isIntegralElem_root_of_map",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1119"
        },
        {
          "kind": "lemma",
          "line": 1131,
          "name": "map_mk",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1131"
        },
        {
          "kind": "lemma",
          "line": 1143,
          "name": "AdjoinRoot.map_comp_algebraMap",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1143"
        },
        {
          "kind": "theorem",
          "line": 1161,
          "name": "Algebra.norm_prod",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1161"
        },
        {
          "kind": "theorem",
          "line": 1169,
          "name": "Algebra.norm_pi",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1169"
        },
        {
          "kind": "abbrev",
          "line": 1205,
          "name": "Factors",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1205"
        },
        {
          "kind": "lemma",
          "line": 1209,
          "name": "monic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1209"
        },
        {
          "kind": "lemma",
          "line": 1211,
          "name": "irreducible",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1211"
        },
        {
          "kind": "lemma",
          "line": 1213,
          "name": "dvd",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1213"
        },
        {
          "kind": "lemma",
          "line": 1216,
          "name": "coe_eq",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1216"
        },
        {
          "kind": "def",
          "line": 1221,
          "name": "unique",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1221"
        },
        {
          "kind": "lemma",
          "line": 1225,
          "name": "ne_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1225"
        },
        {
          "kind": "lemma",
          "line": 1227,
          "name": "prime",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1227"
        },
        {
          "kind": "lemma",
          "line": 1229,
          "name": "separable",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1229"
        },
        {
          "kind": "lemma",
          "line": 1234,
          "name": "mem_normalizedFactors_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1234"
        },
        {
          "kind": "lemma",
          "line": 1240,
          "name": "finite",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1240"
        },
        {
          "kind": "lemma",
          "line": 1248,
          "name": "nonempty",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1248"
        },
        {
          "kind": "def",
          "line": 1253,
          "name": "linearEquivRoots",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1253"
        },
        {
          "kind": "lemma",
          "line": 1271,
          "name": "isCoprime",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Basic.lean#L1271"
        },
        {
          "kind": "lemma",
          "line": 1279,
          "name": "isCoprime_span",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/FormalGroupLaw/Basic.lean#L129"
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          "kind": "lemma",
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          "kind": "theorem",
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          "name": "diffMatrixInv_map_constantCoeff",
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          "kind": "def",
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          "kind": "lemma",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/FormalGroupLaw/Invariance.lean#L579"
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      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/FormalGroupLaw/Invariance.lean"
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        },
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        },
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/FormalGroupLaw/Log.lean#L165"
        },
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        },
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          "kind": "lemma",
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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/MvPSeries.lean#L284"
        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "def",
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          "name": "evalRingHom",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/MvPSeries.lean#L400"
        },
        {
          "kind": "theorem",
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          "name": "coe_evalRingHom",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/MvPSeries.lean#L403"
        },
        {
          "kind": "theorem",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/MvPSeries.lean#L407"
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        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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        }
      ],
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    },
    {
      "declarations": [
        {
          "kind": "theorem",
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        {
          "kind": "def",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "def",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "def",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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          "name": "constantCoeff_iterInv",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/EllipticCurves/Mathlib/Chabauty/MvPowerSeriesComp.lean#L206"
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        }
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "def",
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          "kind": "theorem",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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        {
          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
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        },
        {
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          "kind": "lemma",
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          "kind": "lemma",
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        },
        {
          "kind": "def",
          "line": 130,
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        },
        {
          "kind": "def",
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          "name": "veluSevenU0",
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        },
        {
          "kind": "def",
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          "name": "veluSevenTB",
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        },
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          "kind": "def",
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          "name": "veluSevenUB",
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        },
        {
          "kind": "def",
          "line": 142,
          "name": "veluSevenTC",
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        },
        {
          "kind": "def",
          "line": 145,
          "name": "veluSevenUC",
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        },
        {
          "kind": "def",
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        },
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          "kind": "def",
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        },
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          "kind": "def",
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        },
        {
          "kind": "def",
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        },
        {
          "kind": "def",
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          "kind": "def",
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          "kind": "theorem",
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          "kind": "theorem",
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        {
          "kind": "theorem",
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          "name": "orderSevenVelu_completedSquare",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L243"
        },
        {
          "kind": "theorem",
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          "name": "equation_iff_completedSquare",
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        },
        {
          "kind": "theorem",
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          "name": "orderSevenVelu_equation",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L284"
        },
        {
          "kind": "def",
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          "name": "OrderSevenKernelX",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L310"
        },
        {
          "kind": "instance",
          "line": 313,
          "name": "orderSevenKernelXDecidable",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L313"
        },
        {
          "kind": "theorem",
          "line": 320,
          "name": "orderSevenOrigin_nonsingular",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L320"
        },
        {
          "kind": "def",
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        },
        {
          "kind": "theorem",
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          "name": "orderSevenFamily_parameters_ne",
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        },
        {
          "kind": "theorem",
          "line": 357,
          "name": "orderSevenFrickeParameter_ne_zero",
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        },
        {
          "kind": "theorem",
          "line": 364,
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        },
        {
          "kind": "theorem",
          "line": 373,
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        },
        {
          "kind": "theorem",
          "line": 384,
          "name": "seven_nsmul_orderSevenOrigin",
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        },
        {
          "kind": "theorem",
          "line": 433,
          "name": "addOrderOf_orderSevenOrigin",
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        },
        {
          "kind": "def",
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        },
        {
          "kind": "def",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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          "name": "orderSevenPointMap_some_of_not_kernelX",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L472"
        },
        {
          "kind": "theorem",
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          "name": "orderSevenPointMap_some_eq_zero_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L485"
        },
        {
          "kind": "theorem",
          "line": 497,
          "name": "orderSevenPointMap_origin",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean#L497"
        },
        {
          "kind": "theorem",
          "line": 504,
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        },
        {
          "kind": "theorem",
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          "name": "orderSevenPointMap_kernel_killed_by_seven",
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        },
        {
          "kind": "theorem",
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          "name": "addOrderOf_orderSevenPointMap_of_order_fortyNine",
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        },
        {
          "kind": "theorem",
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          "name": "exists_orderSevenHauptmodul_of_order_fortyNine_image",
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        },
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          "kind": "theorem",
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        }
      ],
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      "imports": [
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        "Mathlib.Tactic.FieldSimp"
      ],
      "lines": 652,
      "module": "MazurTorsion.Kubert.OrderSevenIsogeny",
      "path": "MazurTorsion/Kubert/OrderSevenIsogeny.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenIsogeny.lean"
    },
    {
      "declarations": [
        {
          "kind": "theorem",
          "line": 35,
          "name": "orderSeven_tate_relation",
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        },
        {
          "kind": "theorem",
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          "name": "orderSeven_parametrization",
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        },
        {
          "kind": "theorem",
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          "name": "orderSeven_\u0394",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenParametrization.lean#L111"
        },
        {
          "kind": "theorem",
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          "name": "orderSeven_c\u2084",
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        },
        {
          "kind": "theorem",
          "line": 132,
          "name": "orderSeven_hauptmodul_identity",
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        }
      ],
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      "lines": 149,
      "module": "MazurTorsion.Kubert.OrderSevenParametrization",
      "path": "MazurTorsion/Kubert/OrderSevenParametrization.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSevenParametrization.lean"
    },
    {
      "declarations": [
        {
          "kind": "def",
          "line": 39,
          "name": "normalizedCurve",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L39"
        },
        {
          "kind": "lemma",
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          "name": "normalized_curve_equation",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L42"
        },
        {
          "kind": "lemma",
          "line": 50,
          "name": "normalized_duplication_identity_algebra",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L50"
        },
        {
          "kind": "lemma",
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        },
        {
          "kind": "lemma",
          "line": 113,
          "name": "isCoprime_sub_sq_left",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L113"
        },
        {
          "kind": "lemma",
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          "name": "isCoprime_add_sq_left",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L120"
        },
        {
          "kind": "lemma",
          "line": 127,
          "name": "odd_sq_sub_sq_of_opposite_parity",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L127"
        },
        {
          "kind": "lemma",
          "line": 158,
          "name": "odd_sq_add_sq_of_opposite_parity",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L158"
        },
        {
          "kind": "lemma",
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          "name": "odd_sub_of_opposite_parity",
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        },
        {
          "kind": "lemma",
          "line": 210,
          "name": "opposite_parity_pairwise_coprime",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L210"
        },
        {
          "kind": "theorem",
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          "name": "no_opposite_parity_certificate",
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        },
        {
          "kind": "lemma",
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          "name": "opposite_parity_of_odd_sum",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L315"
        },
        {
          "kind": "theorem",
          "line": 323,
          "name": "no_odd_odd_certificate",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L323"
        },
        {
          "kind": "lemma",
          "line": 461,
          "name": "integral_certificate_of_sextic_solution",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L461"
        },
        {
          "kind": "theorem",
          "line": 503,
          "name": "no_nondegenerate_sextic_solution",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L503"
        },
        {
          "kind": "lemma",
          "line": 548,
          "name": "sextic_solution_of_square_relation",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L548"
        },
        {
          "kind": "lemma",
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          "name": "square_relation_of_scaled_duplication",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L594"
        },
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          "kind": "theorem",
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          "name": "no_scaled_duplication_chain",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L609"
        },
        {
          "kind": "lemma",
          "line": 623,
          "name": "first_scaled_identity",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L623"
        },
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          "kind": "lemma",
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          "name": "second_scaled_identity",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L630"
        },
        {
          "kind": "lemma",
          "line": 638,
          "name": "quotient_square_of_duplication",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderSixteenReduction.lean#L638"
        },
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          "kind": "theorem",
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          "name": "no_normalized_coordinate_duplication_chain_aux",
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        },
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          "kind": "theorem",
          "line": 737,
          "name": "no_normalized_coordinate_duplication_chain",
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        },
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          "kind": "lemma",
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        {
          "kind": "lemma",
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          "name": "tl_mnum\u2083",
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      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneX.lean"
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps0To2.lean#L38"
        },
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          "kind": "lemma",
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          "name": "tlWOneX_s2",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps0To2.lean#L61"
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      "module": "MazurTorsion.Kubert.OrderTwentySevenLegStagesB.WOneXSteps0To2",
      "path": "MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps0To2.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps0To2.lean"
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      "declarations": [
        {
          "kind": "lemma",
          "line": 17,
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          "name": "tlWOneX_s4",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps3To5.lean#L41"
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          "name": "tlWOneX_s5",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps3To5.lean#L65"
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      "module": "MazurTorsion.Kubert.OrderTwentySevenLegStagesB.WOneXSteps3To5",
      "path": "MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps3To5.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WOneXSteps3To5.lean"
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        {
          "kind": "lemma",
          "line": 18,
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WTwoX.lean#L18"
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      "module": "MazurTorsion.Kubert.OrderTwentySevenLegStagesB.WTwoX",
      "path": "MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WTwoX.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WTwoX.lean"
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        }
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      "path": "MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WTwoXSteps0To1.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WTwoXSteps0To1.lean"
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      "path": "MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WZeroX.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WZeroX.lean"
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WZeroXSteps.lean#L56"
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      "module": "MazurTorsion.Kubert.OrderTwentySevenLegStagesB.WZeroXSteps",
      "path": "MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WZeroXSteps.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/WZeroXSteps.lean"
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          "name": "tlRowCell11",
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          "name": "tlRowCell12",
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          "name": "tlRowCell13",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1048"
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          "name": "tlRowCell14",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1102"
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          "kind": "def",
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          "name": "tlRowCell15",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1130"
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        {
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          "name": "tlRowCell16",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1174"
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          "name": "tl_row0",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1202"
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          "name": "tl_row1",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1224"
        },
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          "name": "tl_row2",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1250"
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1282"
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1316"
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          "name": "tl_row5",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1351"
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          "name": "tl_row6",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1386"
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1421"
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          "name": "tl_row8",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1455"
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          "name": "tl_row9",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1489"
        },
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          "name": "tl_row10",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1524"
        },
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          "name": "tl_row11",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1541"
        },
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          "name": "tl_row12",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1578"
        },
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          "name": "tl_row13",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1598"
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          "name": "tl_row14",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1635"
        },
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          "name": "tl_row15",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1665"
        },
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          "name": "tl_row16",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1702"
        },
        {
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          "name": "tlColumn",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1711"
        },
        {
          "kind": "lemma",
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          "name": "tl_rows_as_columns",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1721"
        },
        {
          "kind": "lemma",
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          "name": "tl_row_major",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1741"
        },
        {
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          "name": "tl_col0",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1750"
        },
        {
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          "name": "tl_col1",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1760"
        },
        {
          "kind": "lemma",
          "line": 1770,
          "name": "tl_col2",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1770"
        },
        {
          "kind": "lemma",
          "line": 1780,
          "name": "tl_col3",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1780"
        },
        {
          "kind": "lemma",
          "line": 1790,
          "name": "tl_col4",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/Kubert/OrderTwentySevenLegStagesB/Zero.lean#L1790"
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          "kind": "lemma",
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      "path": "MazurTorsion/NumberTheory/SevenAdicCertificates.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/SevenAdicCertificates.lean"
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          "kind": "theorem",
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        },
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          "kind": "def",
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          "kind": "theorem",
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          "name": "eisensteinPiDivides_iff",
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        },
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          "kind": "theorem",
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          "name": "seven_dvd_eisensteinNorm_of_piDivides",
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          "kind": "theorem",
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        },
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          "name": "piParameterForm",
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          "name": "parameter_forms_m_identity",
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          "name": "parameter_forms_n_identity",
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          "kind": "lemma",
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          "name": "common_zero_mod_seven",
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        "Mathlib.RingTheory.Polynomial.RationalRoot"
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      "lines": 626,
      "module": "MazurTorsion.NumberTheory.XOneEighteenDescent",
      "path": "MazurTorsion/NumberTheory/XOneEighteenDescent.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenDescent.lean"
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          "kind": "theorem",
          "line": 156,
          "name": "invariantY_orderThree",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L156"
        },
        {
          "kind": "theorem",
          "line": 168,
          "name": "invariant_conic_equation",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L168"
        },
        {
          "kind": "abbrev",
          "line": 184,
          "name": "F5",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L184"
        },
        {
          "kind": "def",
          "line": 188,
          "name": "sextic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L188"
        },
        {
          "kind": "def",
          "line": 192,
          "name": "sexticValue",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L192"
        },
        {
          "kind": "lemma",
          "line": 197,
          "name": "eval_sextic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L197"
        },
        {
          "kind": "lemma",
          "line": 203,
          "name": "sexticValue_eq_model_formula",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L203"
        },
        {
          "kind": "lemma",
          "line": 209,
          "name": "five_eq_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L209"
        },
        {
          "kind": "lemma",
          "line": 211,
          "name": "six_eq_one",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L211"
        },
        {
          "kind": "lemma",
          "line": 213,
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        },
        {
          "kind": "lemma",
          "line": 216,
          "name": "polynomial_eleven_eq_one",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L216"
        },
        {
          "kind": "lemma",
          "line": 222,
          "name": "polynomial_fifteen_eq_zero",
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        },
        {
          "kind": "lemma",
          "line": 229,
          "name": "derivative_sextic",
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        },
        {
          "kind": "def",
          "line": 235,
          "name": "bezoutLeft",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L235"
        },
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          "kind": "def",
          "line": 239,
          "name": "bezoutRight",
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        },
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          "kind": "lemma",
          "line": 243,
          "name": "sextic_derivative_bezout",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L243"
        },
        {
          "kind": "theorem",
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          "name": "sextic_isCoprime_derivative",
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        },
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          "kind": "theorem",
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          "name": "sextic_separable",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L257"
        },
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          "kind": "theorem",
          "line": 261,
          "name": "sextic_squarefree",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L261"
        },
        {
          "kind": "theorem",
          "line": 265,
          "name": "sextic_or_derivative_ne_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L265"
        },
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          "kind": "def",
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          "name": "AffineSolution",
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        },
        {
          "kind": "theorem",
          "line": 290,
          "name": "affine_solution_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L290"
        },
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          "kind": "theorem",
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        },
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          "kind": "theorem",
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          "name": "card_affineSolution",
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        },
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          "kind": "def",
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          "name": "IsAffineCuspX",
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        },
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          "kind": "theorem",
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          "name": "affine_solution_is_cusp_value",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L318"
        },
        {
          "kind": "theorem",
          "line": 325,
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        },
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          "kind": "theorem",
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          "name": "cusp_abscissa_solution_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L333"
        },
        {
          "kind": "lemma",
          "line": 342,
          "name": "eval_derivative_sextic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L342"
        },
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          "kind": "theorem",
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          "name": "affine_jacobian_nonsingular",
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        },
        {
          "kind": "theorem",
          "line": 355,
          "name": "affine_jacobian_nonsingular_polynomial",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L355"
        },
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          "kind": "theorem",
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          "name": "sextic_monic",
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        },
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          "kind": "def",
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          "name": "InfinityDirection",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L370"
        },
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          "kind": "theorem",
          "line": 379,
          "name": "infinity_equation_iff_leadingCoeff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L379"
        },
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          "kind": "theorem",
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          "name": "infinity_direction_satisfies_leadingCoeff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L385"
        },
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          "kind": "theorem",
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          "name": "infinity_direction_iff",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L391"
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          "name": "card_infinityDirection",
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        },
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        },
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          "kind": "def",
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          "name": "PointCertificate",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L414"
        },
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          "kind": "theorem",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean#L423"
        }
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      "imports": [
        "MazurTorsion.Kubert.OrderEighteenModel",
        "Mathlib.Data.Fintype.Sets",
        "Mathlib.FieldTheory.Separable"
      ],
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      "module": "MazurTorsion.NumberTheory.XOneEighteenFiniteField",
      "path": "MazurTorsion/NumberTheory/XOneEighteenFiniteField.lean",
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    },
    {
      "declarations": [
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          "kind": "theorem",
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          "name": "fg_point_of_finiteIndex_five",
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        },
        {
          "kind": "def",
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        },
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          "kind": "theorem",
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          "name": "double_P00",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L112"
        },
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          "kind": "theorem",
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          "name": "add_P00_P1n1",
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        },
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          "kind": "theorem",
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          "name": "triple_P00",
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        },
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          "kind": "theorem",
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          "name": "double_P1n1",
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        },
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          "name": "four_P00",
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        },
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          "name": "five_P00",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L173"
        },
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        },
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          "kind": "def",
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          "name": "fiveIsogenousCurve",
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        },
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          "kind": "def",
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          "name": "veluFiveX",
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        },
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          "kind": "def",
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          "name": "veluFiveY",
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        },
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        },
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          "kind": "def",
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        },
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          "kind": "def",
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          "name": "veluFiveMap",
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        },
        {
          "kind": "def",
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          "name": "fiveKummerFunction",
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        },
        {
          "kind": "abbrev",
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          "name": "FiveTorsion",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L314"
        },
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          "kind": "def",
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          "name": "fiveTorsionReduction",
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        },
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          "name": "fiveTorsionReduction_injective",
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          "name": "five_torsion_card_le_five",
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        },
        {
          "kind": "def",
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          "name": "visibleFiveTorsion",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L371"
        },
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          "name": "visibleFiveTorsion_injective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L383"
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          "name": "five_torsion_card_eq_five",
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        },
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          "name": "visibleFiveTorsion_bijective",
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        },
        {
          "kind": "def",
          "line": 418,
          "name": "fiveRepresentative",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L418"
        },
        {
          "kind": "def",
          "line": 429,
          "name": "FiveCosetBound",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneElevenDescent.lean#L429"
        },
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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "def",
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          "kind": "def",
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          "kind": "def",
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          "kind": "def",
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          "kind": "instance",
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        },
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          "kind": "abbrev",
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          "name": "redTwo",
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          "name": "no_dual_three_class",
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        },
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          "name": "no_dual_neg_five_class",
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        },
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          "name": "no_quartic_rat_of_no_int",
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          "name": "no_curve_two_class_rat",
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          "name": "no_dual_neg_one_class_rat",
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          "name": "no_dual_neg_five_class_rat",
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          "name": "no_dual_fifteen_class_rat",
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          "name": "common_divisor_dual_dvd_fifteen",
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        },
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          "kind": "lemma",
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          "name": "squareclass_of_gcd_dvd_fifteen",
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          "line": 385,
          "name": "dual_abscissa_squareclass",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L385"
        },
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          "kind": "theorem",
          "line": 469,
          "name": "dual_abscissa_visible_squareclasses",
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        },
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          "kind": "lemma",
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          "name": "common_divisor_curve_dvd_sixteen",
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        },
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          "kind": "lemma",
          "line": 554,
          "name": "positive_squareclass_of_gcd_dvd_sixteen",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L554"
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "theorem",
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          "kind": "theorem",
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          "kind": "theorem",
          "line": 918,
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L918"
        },
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          "kind": "lemma",
          "line": 1000,
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        },
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          "kind": "lemma",
          "line": 1005,
          "name": "nonsingular_four_four",
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        },
        {
          "kind": "lemma",
          "line": 1010,
          "name": "nonsingular_four_neg_four",
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        },
        {
          "kind": "def",
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          "name": "T",
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          "kind": "def",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1020"
        },
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          "kind": "lemma",
          "line": 1023,
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1023"
        },
        {
          "kind": "lemma",
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          "kind": "lemma",
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        },
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          "kind": "lemma",
          "line": 1051,
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1051"
        },
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          "kind": "lemma",
          "line": 1062,
          "name": "translated_y_identity",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1062"
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          "kind": "lemma",
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        },
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          "kind": "lemma",
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        },
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          "kind": "lemma",
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        },
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          "kind": "theorem",
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        },
        {
          "kind": "lemma",
          "line": 1313,
          "name": "curve_equation_of_nonsingular",
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        },
        {
          "kind": "theorem",
          "line": 1323,
          "name": "two_doubling_cosets",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1323"
        },
        {
          "kind": "abbrev",
          "line": 1388,
          "name": "doublingRange",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1388"
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        {
          "kind": "def",
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        },
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          "kind": "lemma",
          "line": 1395,
          "name": "doubling_quotient_surjective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1395"
        },
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          "kind": "theorem",
          "line": 1414,
          "name": "doubling_finiteIndex",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1414"
        },
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          "kind": "theorem",
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          "name": "point_fg",
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          "kind": "theorem",
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          "name": "doubling_index_le_two",
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          "kind": "def",
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          "kind": "lemma",
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          "name": "twoToTwoTorsion_injective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFifteenDescent.lean#L1436"
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          "kind": "lemma",
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          "kind": "theorem",
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          "kind": "theorem",
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      "path": "MazurTorsion/NumberTheory/XOneFifteenDescent.lean",
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      "declarations": [
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          "kind": "lemma",
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          "kind": "lemma",
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          "name": "orderEightPolynomial",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L43"
        },
        {
          "kind": "def",
          "line": 56,
          "name": "intPrime",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L56"
        },
        {
          "kind": "lemma",
          "line": 62,
          "name": "intPrime_asIdeal",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L62"
        },
        {
          "kind": "lemma",
          "line": 70,
          "name": "isElliptic_redCurve",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L70"
        },
        {
          "kind": "def",
          "line": 88,
          "name": "curveModThree",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L88"
        },
        {
          "kind": "def",
          "line": 96,
          "name": "residueThreeAlgEquiv",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L96"
        },
        {
          "kind": "lemma",
          "line": 106,
          "name": "baseChange_modThree",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L106"
        },
        {
          "kind": "def",
          "line": 114,
          "name": "reducedPointEquiv",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L114"
        },
        {
          "kind": "theorem",
          "line": 127,
          "name": "card_reducedCurve",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L127"
        },
        {
          "kind": "lemma",
          "line": 138,
          "name": "three_mem_prime",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L138"
        },
        {
          "kind": "lemma",
          "line": 142,
          "name": "three_not_mem_prime_pow_two",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L142"
        },
        {
          "kind": "theorem",
          "line": 149,
          "name": "reduction_injective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L149"
        },
        {
          "kind": "theorem",
          "line": 164,
          "name": "point_card_le_six",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L164"
        },
        {
          "kind": "theorem",
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          "name": "sixVisiblePoints_bijective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L178"
        },
        {
          "kind": "theorem",
          "line": 187,
          "name": "point_abscissa_eq_zero_four_or_eight",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean#L187"
        }
      ],
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      "imports": [
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        "MazurTorsion.NumberTheory.XOneFourteenDescent"
      ],
      "lines": 224,
      "module": "MazurTorsion.NumberTheory.XOneFourteenReduction",
      "path": "MazurTorsion/NumberTheory/XOneFourteenReduction.lean",
      "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneFourteenReduction.lean"
    },
    {
      "declarations": [
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          "kind": "lemma",
          "line": 50,
          "name": "add_one_ne_zero",
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        },
        {
          "kind": "def",
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          "name": "diamondX",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L59"
        },
        {
          "kind": "def",
          "line": 63,
          "name": "diamondY",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L63"
        },
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          "kind": "theorem",
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          "name": "diamond_sextic_covariance",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L68"
        },
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          "kind": "theorem",
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          "name": "diamond_preserves_curve",
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        },
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          "kind": "theorem",
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          "name": "diamondX_sq",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L96"
        },
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          "kind": "theorem",
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          "name": "diamondX_cube",
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        },
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          "kind": "theorem",
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          "name": "diamondY_sq",
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        },
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          "kind": "theorem",
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          "name": "diamondY_cube",
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        },
        {
          "kind": "theorem",
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          "name": "diamondY_cube_ne",
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        },
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          "kind": "def",
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        },
        {
          "kind": "def",
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          "name": "quotientV",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L153"
        },
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          "kind": "theorem",
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          "name": "quotientU_diamond",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L157"
        },
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          "kind": "theorem",
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        },
        {
          "kind": "theorem",
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        },
        {
          "kind": "def",
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        },
        {
          "kind": "def",
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          "name": "conicV",
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        },
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          "kind": "theorem",
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          "name": "conic_parameter_equation",
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        },
        {
          "kind": "def",
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          "name": "conicSlope",
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        },
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          "kind": "lemma",
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          "name": "conicSlope_sq_ne_one",
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        },
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          "name": "conic_parameter_inverse",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L239"
        },
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        },
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          "kind": "theorem",
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        },
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          "name": "fiberCubic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L299"
        },
        {
          "kind": "def",
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          "name": "exceptionalFiberPolynomial",
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        },
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          "kind": "lemma",
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          "name": "exceptionalFiberPolynomial_monic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L308"
        },
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          "kind": "lemma",
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          "name": "exceptionalFiberPolynomial_no_root_mod_two",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L313"
        },
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          "kind": "theorem",
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          "name": "fiberCubic_neg_one_ne_zero",
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        },
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          "kind": "theorem",
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          "name": "fiberCubic_quotientU",
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        },
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          "kind": "theorem",
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          "name": "quotientU_ne_neg_one",
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        },
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          "kind": "def",
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          "name": "orbitNorm",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L365"
        },
        {
          "kind": "theorem",
          "line": 371,
          "name": "orbitNorm_eq_fiberCubic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L371"
        },
        {
          "kind": "def",
          "line": 384,
          "name": "cubicDiscriminant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L384"
        },
        {
          "kind": "theorem",
          "line": 389,
          "name": "fiberCubic_discriminant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L389"
        },
        {
          "kind": "def",
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          "name": "clearedFiber",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L396"
        },
        {
          "kind": "theorem",
          "line": 403,
          "name": "clearedFiber_eq_mul_fiberCubic",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L403"
        },
        {
          "kind": "theorem",
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          "name": "clearedFiber_eq_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L414"
        },
        {
          "kind": "def",
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          "name": "parameterDiscriminant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L421"
        },
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          "kind": "theorem",
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          "name": "clearedFiber_discriminant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L426"
        },
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          "name": "fiber_discriminant_parameter_factorization",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L437"
        },
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          "name": "homogeneousFiber",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L448"
        },
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          "kind": "theorem",
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          "name": "homogeneousFiber_eq_den_sq_mul",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L456"
        },
        {
          "kind": "def",
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          "name": "homogeneousDiscriminant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L464"
        },
        {
          "kind": "theorem",
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          "name": "homogeneousFiber_discriminant",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L469"
        },
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          "kind": "theorem",
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          "name": "noncuspidal_curve_parameterization",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L481"
        },
        {
          "kind": "theorem",
          "line": 504,
          "name": "noncuspidal_curve_primitive_parameterization",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L504"
        },
        {
          "kind": "def",
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          "name": "sixthRootMul",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L535"
        },
        {
          "kind": "def",
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          "name": "sixthRootNorm",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L540"
        },
        {
          "kind": "def",
          "line": 544,
          "name": "sixthRootRho",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L544"
        },
        {
          "kind": "theorem",
          "line": 548,
          "name": "sixthRootRho_relation",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L548"
        },
        {
          "kind": "theorem",
          "line": 554,
          "name": "sixthRootNorm_mul",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L554"
        },
        {
          "kind": "def",
          "line": 563,
          "name": "sixthRootConj",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L563"
        },
        {
          "kind": "theorem",
          "line": 567,
          "name": "sixthRootMul_conj",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XOneThirteenDescent.lean#L567"
        },
        {
          "kind": "theorem",
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          "name": "sixthRootNorm_conj",
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          "kind": "def",
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        },
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          "kind": "theorem",
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        },
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          "kind": "theorem",
          "line": 655,
          "name": "nineteen_dvd_sixthRootNorm_of_piDivides",
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        },
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          "kind": "theorem",
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          "kind": "lemma",
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          "kind": "theorem",
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        },
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          "kind": "theorem",
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        },
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        },
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        },
        {
          "kind": "theorem",
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        },
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          "kind": "def",
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        },
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          "kind": "def",
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          "name": "infinityPellH",
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        },
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          "kind": "def",
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        },
        {
          "kind": "theorem",
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          "name": "infinityPellH_eq_reciprocal",
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        },
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          "kind": "theorem",
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        },
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        }
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        "Mathlib.RingTheory.Polynomial.RationalRoot"
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      "declarations": [
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          "kind": "def",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L85"
        },
        {
          "kind": "lemma",
          "line": 91,
          "name": "intCast_reduceTwoOfFour_ne_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L91"
        },
        {
          "kind": "lemma",
          "line": 100,
          "name": "two_dvd_of_two_dvd_sq",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L100"
        },
        {
          "kind": "lemma",
          "line": 106,
          "name": "no_dual_two_class_int",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L106"
        },
        {
          "kind": "lemma",
          "line": 169,
          "name": "no_dual_two_class_rat",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L169"
        },
        {
          "kind": "lemma",
          "line": 195,
          "name": "common_divisor_dual_dvd_256",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L195"
        },
        {
          "kind": "lemma",
          "line": 217,
          "name": "squareclass_of_gcd_dvd_256",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L217"
        },
        {
          "kind": "theorem",
          "line": 285,
          "name": "dual_abscissa_isSquare",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L285"
        },
        {
          "kind": "lemma",
          "line": 406,
          "name": "y_linear_of_reverse_definition",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L406"
        },
        {
          "kind": "lemma",
          "line": 413,
          "name": "y_formula_of_reverse_linear",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L413"
        },
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          "kind": "lemma",
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          "name": "y_formula_squared",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L422"
        },
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          "kind": "theorem",
          "line": 432,
          "name": "double_of_square_abscissa",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L432"
        },
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          "kind": "theorem",
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          "name": "abscissa_class_of_ne_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L596"
        },
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          "kind": "lemma",
          "line": 637,
          "name": "nonsingular_zero_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L637"
        },
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          "kind": "lemma",
          "line": 641,
          "name": "nonsingular_nine_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L641"
        },
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          "kind": "lemma",
          "line": 645,
          "name": "nonsingular_negSeven_zero",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L645"
        },
        {
          "kind": "lemma",
          "line": 649,
          "name": "nonsingular_negThree_twelve",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L649"
        },
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          "kind": "lemma",
          "line": 653,
          "name": "nonsingular_negThree_negTwelve",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L653"
        },
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          "kind": "lemma",
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          "name": "nonsingular_twentyOne_eightyFour",
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        },
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          "kind": "lemma",
          "line": 661,
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          "kind": "def",
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        },
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          "kind": "def",
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        },
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          "kind": "def",
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        },
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          "kind": "def",
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          "name": "P\u2083",
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        },
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          "kind": "def",
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        },
        {
          "kind": "def",
          "line": 686,
          "name": "P\u2082\u2081",
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        },
        {
          "kind": "def",
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        },
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          "kind": "lemma",
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          "name": "negY_eq",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L693"
        },
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          "kind": "lemma",
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          "name": "neg_T",
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        },
        {
          "kind": "lemma",
          "line": 702,
          "name": "neg_P\u2083",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L702"
        },
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          "kind": "lemma",
          "line": 707,
          "name": "neg_P\u2082\u2081",
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          "kind": "theorem",
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          "kind": "theorem",
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          "name": "P\u2082\u2081_add_T",
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        },
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          "kind": "lemma",
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          "name": "decompose_of_sub_eq_some",
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          "kind": "lemma",
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        },
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          "kind": "lemma",
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          "name": "decompose_affine_rep",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L811"
        },
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          "kind": "theorem",
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          "name": "four_doubling_cosets",
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        },
        {
          "kind": "abbrev",
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          "name": "doublingRange",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1035"
        },
        {
          "kind": "def",
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          "name": "doublingRepresentative",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1038"
        },
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          "kind": "lemma",
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          "name": "doubling_quotient_surjective",
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        },
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          "kind": "theorem",
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          "name": "doubling_finiteIndex",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1073"
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        {
          "kind": "theorem",
          "line": 1079,
          "name": "point_fg",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1079"
        },
        {
          "kind": "theorem",
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          "name": "doubling_index_le_four",
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        },
        {
          "kind": "lemma",
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          "name": "double_T",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1092"
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          "kind": "lemma",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1098"
        },
        {
          "kind": "lemma",
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          "name": "double_T\u2087",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1104"
        },
        {
          "kind": "def",
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          "kind": "lemma",
          "line": 1117,
          "name": "fourToTwoTorsion_injective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1117"
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          "kind": "lemma",
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          "name": "fourToTwoTorsion_surjective",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1124"
        },
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          "kind": "theorem",
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          "name": "two_torsion_card_eq_four",
          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1160"
        },
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          "kind": "theorem",
          "line": 1173,
          "name": "point_rank_zero",
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          "kind": "theorem",
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        },
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          "kind": "def",
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          "source_url": "https://github.com/Vilin97/MazurTheorem/blob/4d20ee38bc71dbaf866d9956f305e8b21f4a9e52/MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean#L1218"
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          "kind": "theorem",
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          "name": "eightVisiblePoints_injective",
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      "path": "MazurTorsion/NumberTheory/XZeroTwentyOneRankZero.lean",
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          "kind": "def",
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          "kind": "lemma",
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          "kind": "lemma",
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          "kind": "lemma",
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