file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.measurable_of_not_zero_le_restrict | [] | [
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Mathlib/LinearAlgebra/AffineSpace/Slope.lean | slope_comm | [
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"tactic": "rw [slope, slope, ← neg_vsub_eq_vsub_rev, smul_neg, ← neg_smul, n... | [
96,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivAt.ccosh | [] | [
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Mathlib/Data/Finset/Basic.lean | Finset.sdiff_self | [] | [
2087,
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2086,
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Mathlib/Data/Finset/Pairwise.lean | List.pairwise_iff_coe_toFinset_pairwise | [
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Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_mono | [] | [
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Mathlib/Topology/Algebra/Order/Floor.lean | continuousOn_ceil | [] | [
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Mathlib/Analysis/Calculus/MeanValue.lean | strictConvexOn_of_deriv2_pos' | [] | [
1238,
77
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Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_antiperiod | [
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"tactic": "simpa only [sub_eq_add_neg] using h1.add_antiperiod ... | [
523,
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Mathlib/Combinatorics/Derangements/Basic.lean | derangements.Equiv.RemoveNone.fiber_some | [
{
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... | [
172,
28
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142,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.mul_isLittleO | [
{
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1596,
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1591,
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Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_iUnion_of_directed | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finset_sum_apply | [
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881,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_iInf | [
{
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227,
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226,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.snd_lineMap | [] | [
619,
28
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618,
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Mathlib/Topology/Algebra/FilterBasis.lean | GroupFilterBasis.one | [] | [
100,
24
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99,
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Mathlib/RingTheory/Algebraic.lean | isAlgebraic_algebraMap_of_isAlgebraic | [
{
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144,
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Mathlib/Order/CompleteLattice.lean | Equiv.iSup_comp | [] | [
645,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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Mathlib/Data/Matrix/Notation.lean | Matrix.row_cons | [
{
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187,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Basic.lean | forall_eq_apply_imp_iff' | [
{
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}
] | [
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814,
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Mathlib/Algebra/Order/Group/Abs.lean | eq_of_abs_sub_eq_zero | [] | [
352,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Sym/Sym2.lean | Sym2.other_mem | [
{
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"tactic": "convert m... | [
371,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/LinearAlgebra/Dual.lean | Subspace.dualLift_of_mem | [
{
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"tactic": "convert dualLift_of_subtype ⟨w... | [
1026,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
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Mathlib/Topology/Algebra/Order/Field.lean | TopologicalRing.of_norm | [
{
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52,
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32,
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Mathlib/Algebra/Star/Order.lean | conjugate_nonneg' | [
{
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"tactic": "simpa only [star_star] using conjugate_nonneg ha (star c)"
}
] | [
178,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/GroupAction/Defs.lean | smul_sub | [
{
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956,
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955,
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Mathlib/Init/Algebra/Order.lean | ne_of_lt | [] | [
105,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
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Mathlib/Data/PEquiv.lean | PEquiv.self_trans_symm | [
{
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281,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
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Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolAlg_symmDiff | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.38685\nγ : Type ?u.38688\ninst✝² : Bool... | [
321,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
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Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Icc_int_cast | [
{
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"tactic": "simpa only [zero_add] using iUnion_Icc_add_int_cast (0 : α)"
}
] | [
1118,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_multiset_sum | [] | [
702,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
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Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_eq_zero_iff | [
{
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"tactic": "simp only [exponentExists_iff_ne_zero, Classical.not_not]"
}
] | [
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60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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Mathlib/Algebra/CharP/Basic.lean | Int.cast_injOn_of_ringChar_ne_two | [
{
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710,
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Mathlib/Computability/Primrec.lean | Primrec.of_equiv_iff | [
{
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310,
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306,
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Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.image_Iio | [
{
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"tactic": "rw [e.image_eq_preimage, e.symm.preimage_Iio, e.symm_symm]"
}
] | [
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61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Cauchy.lean | completeSpace_of_isComplete_univ | [] | [
401,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.eq_X_mul_shift_add_const | [
{
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Ioc | [
{
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}
] | [
68,
101
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Mathlib/LinearAlgebra/Determinant.lean | LinearEquiv.det_trans | [] | [
396,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.ImageMap.factor_map | [
{
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"tactic": "simp"
}
] | [
699,
45
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697,
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Mathlib/Data/Nat/Basic.lean | Nat.pred_eq_sub_one | [] | [
308,
6
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Mathlib/Data/List/Perm.lean | List.Perm.bagInter_left | [
{
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Theory.model_singleton_iff | [
{
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] | [
858,
87
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858,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_iff_forall_tendsto | [
{
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Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAt.sub | [] | [
306,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_same | [
{
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753,
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Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_iff_ne_cons_cons | [
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_left_le_iff | [
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Mathlib/Order/SymmDiff.lean | bihimp_himp_left | [] | [
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.nonempty_def | [] | [
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Mathlib/Algebra/Order/Module.lean | BddAbove.smul_of_nonpos | [] | [
218,
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Mathlib/Data/W/Cardinal.lean | WType.cardinal_mk_le_of_le | [
{
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Mathlib/RingTheory/RingInvo.lean | RingInvo.coe_ringEquiv | [] | [
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Mathlib/Topology/Semicontinuous.lean | ContinuousOn.upperSemicontinuousOn | [] | [
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_congr | [
{
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Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.RanIsSheafOfCoverLifting.gluedLimitCone_π_app | [] | [
214,
6
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213,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_pi_div_two | [
{
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},
{
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{
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1118,
21
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Mathlib/GroupTheory/Congruence.lean | Con.lift_apply_mk' | [
{
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... | [
956,
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954,
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Mathlib/Data/Set/Lattice.lean | Set.image2_iUnion₂_left | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.ι_colimitConstInitial_hom | [
{
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494,
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491,
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.pow_fst | [] | [
323,
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322,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero | [
{
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336,
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332,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_eq_empty_iff | [
{
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}
] | [
80,
53
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.existsUnique | [] | [
1011,
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1009,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasFDerivAt.rpow_const | [] | [
459,
50
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457,
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Mathlib/Data/Nat/Choose/Factorization.lean | Nat.factorization_choose_le_log | [
{
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Mathlib/Data/Stream/Init.lean | Stream'.tail_inits | [
{
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694,
28
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691,
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Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_tsub | [
{
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169,
64
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163,
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Mathlib/Order/BooleanAlgebra.lean | inf_sdiff_distrib_left | [
{
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"tactic": "rw [sdiff_inf, sdiff_eq_bot_iff.2 inf_le_left, bot_sup_eq, inf_sdiff_assoc]"
}
] | [
454,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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Mathlib/Data/Multiset/Basic.lean | Multiset.filter_union | [] | [
2059,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2058,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.mulVecLin_submatrix | [] | [
234,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostFun_int_cast | [
{
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213,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.neg_mem | [
{
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"state_before": "S : Type u'\nT : Type u''\nR : Type u\nM : Type v\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\... | [
360,
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Mathlib/RingTheory/Ideal/Operations.lean | RingHom.ker_ne_top | [] | [
2023,
52
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2022,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.spanSingleton_eq_spanSingleton | [
{
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1323,
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Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_iterate_comp | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\n⊢ natDegree ((comp p^[Nat.zero]) q) = natDegree p ^ Nat.zero * natDegree q\n\ncase succ\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ ... | [
361,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
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Mathlib/Data/Set/Semiring.lean | SetSemiring.up_lt_up | [] | [
81,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/CategoryTheory/Sites/Whiskering.lean | CategoryTheory.GrothendieckTopology.Cover.multicospanComp_app_left | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/RingTheory/IntegralClosure.lean | RingHom.isIntegralElem_of_isIntegralElem_comp | [
{
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"state_before": "R : Type u_1\nA : Type ?u.1572223\nB : Type ?u.1572226\nS : Type u_3\nT : Type u_2\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : CommRing B\ninst✝⁵ : CommRing S\ninst✝⁴ : CommRing T\ninst✝³ : Algebra A B\ninst✝² : Algebra R B\nf : R →+* S\ng : S →+* T\nins... | [
1065,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_finset_sum | [
{
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1395,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
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Mathlib/Data/Nat/PartENat.lean | PartENat.eq_zero_iff | [] | [
336,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
8
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.mul_comp | [] | [
351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.preimage_continuous | [] | [
199,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Control/Functor.lean | Functor.Comp.run_seq | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Real.hasSum_cos | [
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ HasSum (fun n => (-1) ^ n * r ^ (2 * n) / ↑(2 * n)!) (cos r)",
"tactic": "exact_mod_cast Complex.hasSum_cos r"
}
] | [
107,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sum_option_index_smul | [] | [
862,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.bounded_image | [] | [
124,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.prod_factors | [
{
"state_after": "no goals",
"state_before": "⊢ 0 ≠ 0 → List.prod (factors 0) = 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "⊢ 1 ≠ 0 → List.prod (factors 1) = 1",
"tactic": "simp"
},
{
"state_after": "k : ℕ\nx✝ : k + 2 ≠ 0\nm : ℕ := minFac (k + 2)\nthis :... | [
82,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Rel.lean | Rel.mem_preimage | [] | [
180,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rtakeWhile_suffix | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ takeWhile p (reverse l) <+: reverse l",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ rtakeWhile p l <:+ l",
"tactic": "rw [← reverse_prefix, rtakeWhile, reverse_reverse]"
},
{
"state_after": "no goals",
"... | [
218,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpBFamily_le_fp | [] | [
319,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coordChange_apply_snd | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.54393\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.54404\nZ : Type u_3\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace F\nproj : Z → B\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace (TotalSpace E)\ne : Trivialization F proj\nx : Z\ne'... | [
679,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Monotone.convex_ge | [] | [
389,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | Submodule.IsPrincipal.prime_generator_of_isPrime | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : CommRing R\ninst✝¹ : Module R M\nS : Ideal R\ninst✝ : IsPrincipal S\nis_prime : Ideal.IsPrime S\nne_bot : S ≠ ⊥\nx✝¹ x✝ : R\n⊢ generator S ∣ x✝¹ * x✝ → generator S ∣ x✝¹ ∨ generator S ∣ x✝",
"tactic":... | [
143,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Quaternion.lean | Cardinal.mk_quaternion | [] | [
1458,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1457,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.coeFn_injective | [] | [
153,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.triangle | [] | [
1162,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.Bounded.subset_ball_lt | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nX : Type ?u.489346\nι : Type ?u.489349\ninst✝ : PseudoMetricSpace α\nx : α\ns t : Set α\nr✝ : ℝ\nh : Bounded s\na : ℝ\nc : α\nr : ℝ\nhr : s ⊆ closedBall c r\n⊢ ∃ r, a < r ∧ s ⊆ closedBall c r",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.489346\... | [
2352,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2348,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Fix.rec_unique | [
{
"state_after": "case h\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\ng : F α → α\nh : Fix F → α\nhyp : ∀ (x : F (Fix F)), h (mk x) = g (h <$> x)\nx : Fix F\n⊢ rec g x = h x",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\ng : F α → α\nh : Fix F → α\nhyp :... | [
330,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/FieldTheory/Normal.lean | Normal.splits | [] | [
57,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
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