file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.hasFiniteIntegral_prod_iff' | [
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.coe_top | [] | [
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Mathlib/Topology/Instances/ENNReal.lean | isClosed_setOf_lipschitzOnWith | [
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Mathlib/Data/List/FinRange.lean | List.ofFn_eq_pmap | [
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Mathlib/Order/CompleteLattice.lean | binary_relation_sSup_iff | [
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Mathlib/Data/Sym/Basic.lean | Sym.mem_fill_iff | [
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Mathlib/Topology/Maps.lean | IsClosedMap.of_nonempty | [
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Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.lift_sub_lift | [
{
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Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective | [
{
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Mathlib/Topology/Constructions.lean | continuous_inf_dom_right₂ | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_singleton_pow | [
{
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.ediam_cthickening_le | [
{
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.liftCover_restrict | [
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Mathlib/Tactic/Linarith/Lemmas.lean | Linarith.lt_of_lt_of_eq | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.iInf_sup_eq_top | [] | [
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722,
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Mathlib/Algebra/Order/Floor.lean | Int.floor_nat_add | [
{
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"tactic": "rw [← Int.cast_ofNat, floor_int_add]"
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] | [
757,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
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Mathlib/Algebra/GroupPower/Basic.lean | pow_mul | [
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129,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.infinite_pigeonhole | [
{
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Mathlib/Order/Directed.lean | DirectedOn.insert | [
{
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Mathlib/Algebra/Lie/Submodule.lean | LieModuleHom.ker_id | [] | [
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Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_one_left | [] | [
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96
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_eq_snorm' | [
{
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Mathlib/FieldTheory/Fixed.lean | FixedPoints.smul_polynomial | [
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Mathlib/GroupTheory/DoubleCoset.lean | Doset.rel_bot_eq_right_group_rel | [
{
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106,
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Mathlib/Algebra/IndicatorFunction.lean | Set.le_mulIndicator_apply | [] | [
776,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_congr | [
{
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Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.right_triangle | [
{
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Mathlib/Data/List/Sublists.lean | List.sublists_singleton | [] | [
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112,
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_add_period | [
{
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"tactic": "rw [coe_add, ← eq_sub_iff_add_eq', sub_self, coe_period]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_add | [] | [
879,
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Mathlib/Data/Finset/Card.lean | Finset.filter_card_eq | [
{
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285,
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282,
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Mathlib/Init/Data/Bool/Lemmas.lean | Bool.coe_sort_false | [
{
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}
] | [
118,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
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Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.constantCoeff_invUnitsSub | [
{
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"tactic": "rw [← coeff_zero_eq_constantCoeff_apply, coeff_invUnitsSub, zero_add, pow_one]"
}
] | [
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81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.scaleRoots_eval₂_eq_zero | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Icc | [] | [
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34
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_mk | [] | [
88,
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.uniformContinuous_eval | [
{
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Mathlib/Analysis/Calculus/IteratedDeriv.lean | contDiffOn_iff_continuousOn_differentiableOn_deriv | [
{
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184,
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180,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.aestronglyMeasurable | [] | [
618,
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616,
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Mathlib/Data/Nat/Order/Basic.lean | Nat.mod_mul_right_div_self | [
{
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{
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476,
68
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Mathlib/Data/Set/Finite.lean | Set.finite_isTop | [] | [
1423,
32
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1422,
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.mk_apply | [] | [
374,
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373,
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Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Subsemigroup.center_le_centralizer | [] | [
195,
30
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194,
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Mathlib/Order/Filter/SmallSets.lean | Filter.eventually_small_sets' | [] | [
75,
90
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Mathlib/Data/Finset/Option.lean | Option.toFinset_none | [] | [
45,
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_mul_le_left | [
{
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Mathlib/GroupTheory/OrderOfElement.lean | IsOfFinOrder.apply | [
{
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117,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.pow | [
{
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_closedBall | [
{
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117,
74
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116,
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src/lean/Init/Control/Lawful.lean | ExceptT.run_map | [
{
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Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.smul_apply | [] | [
167,
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166,
1
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Mathlib/Analysis/SpecificLimits/Basic.lean | factorial_tendsto_atTop | [] | [
538,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Order/Filter/Pointwise.lean | Filter.eventually_one | [] | [
136,
18
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Mathlib/Order/Disjoint.lean | Codisjoint.of_codisjoint_sup_of_le' | [] | [
363,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
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Mathlib/Algebra/BigOperators/Fin.lean | List.alternatingProd_eq_finset_prod | [
{
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507,
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493,
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src/lean/Init/Classical.lean | Classical.choose_spec | [] | [
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_eq_one | [
{
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132,
17
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130,
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Mathlib/Data/FunLike/Basic.lean | FunLike.ext'_iff | [] | [
176,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_smul | [
{
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1080,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.inner_left_right_finset | [
{
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864,
59
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861,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.exists_coeff_ne_zero | [] | [
824,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
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Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.hasFDerivAt_aeval | [] | [
164,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
11
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Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | toBilin'Aux_toMatrixAux | [
{
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121,
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Mathlib/Algebra/Star/Pi.lean | Function.star_sum_elim | [
{
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78,
75
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivComm_quotQuotMk | [] | [
591,
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589,
1
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_zero_right | [
{
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"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\nin... | [
141,
62
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139,
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.inf_coe | [] | [
416,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
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Mathlib/Order/Filter/Archimedean.lean | tendsto_rat_cast_atTop_iff | [
{
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90,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/Data/Set/MulAntidiagonal.lean | Set.MulAntidiagonal.eq_of_fst_le_fst_of_snd_le_snd | [] | [
115,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.injective | [
{
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109,
67
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Mathlib/Data/List/Rdrop.lean | List.dropWhile_eq_self_iff | [
{
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162,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.tfae_epi | [
{
"state_after": "case tfae_3_to_2\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ Exact f 0 → cokernel.π f = 0\n\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ntfae_3_to_2 : Exact f 0 → cokernel.π f = 0\n⊢ TFAE [Epi f, cokernel.π ... | [
286,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bitwise'_bit_aux | [
{
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403,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
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Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_add_two | [
{
"state_after": "no goals",
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"tactic": "rw [T]"
}
] | [
85,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.tensorHom_app | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.subset_span_trans | [] | [
282,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_pos | [] | [
1081,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_floor_left_pure_sub_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10243\nγ : Type ?u.10246\ninst✝³ : LinearOrderedRing α\ninst✝² : FloorRing α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nn : ℤ\n⊢ Tendsto floor (𝓝[Iio ↑n] ↑n) (pure (n - 1))",
"tactic": "simpa only [ceil_intCast] u... | [
100,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.continuous_fst | [] | [
62,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
8
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.coe_sup | [
{
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371,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.empty_vsub | [] | [
618,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
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Mathlib/Analysis/NormedSpace/Pointwise.lean | disjoint_ball_ball_iff | [
{
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217,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_eq_sup | [
{
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1433,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
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Mathlib/GroupTheory/Nilpotent.lean | mem_upperCentralSeriesStep | [] | [
108,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | adicCompletion.eval_apply | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Set.Subsingleton.measurableSet | [] | [
306,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.one_le_mulIndicator_apply | [] | [
792,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Topology/Constructions.lean | continuous_inl | [] | [
884,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.integralNormalization_coeff_ne_natDegree | [] | [
81,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_iSup_sum | [] | [
793,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
11
] |
Mathlib/Order/RelClasses.lean | IsIrrefl.swap | [] | [
76,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.iterate_map_mul | [] | [
59,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.Reachable.dist_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\nhr : Reachable G u v\n⊢ dist G u v = 0 ↔ u = v",
"tactic": "simp [hr]"
}
] | [
81,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.ofHamming_toHamming | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infEdist_le_infEdist_cthickening_add | [
{
"state_after": "ι : Sort ?u.150279\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns t : Set α\nx : α\nr : ℝ≥0∞\nh : infEdist x (cthickening δ s) + ENNReal.ofReal δ < r\n⊢ infEdist x s < r",
"state_before": "ι : Sort ?u.150279\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\... | [
1451,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/RingTheory/WittVector/Teichmuller.lean | WittVector.teichmuller_zero | [
{
"state_after": "case h.succ\np : ℕ\nR : Type u_1\nS : Type ?u.163480\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn✝ : ℕ\n⊢ coeff (↑(teichmuller p) 0) (Nat.succ n✝) = 0",
"state_before": "case h.succ\np : ℕ\nR : Type u_1\nS : Type ?u.163480\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing... | [
125,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iInter₂_vsub_subset | [] | [
744,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.inl_snd | [] | [
803,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.cos_eq_cos_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos x - cos y = 0 ↔ -2 * sin ((x + y) / 2) * sin ((x - y) / 2) = 0",
"tactic": "rw [cos_sub_cos]"
},
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ -2 * sin ((x + y) / 2) * sin ((x - y) / 2) = 0 ↔ sin ((x + y) / 2) = 0 ∨ sin ... | [
94,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.div | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.52269\ninst✝¹ : Semifield R\ninst✝ : StarRing R\nx y : R\nhx : IsSelfAdjoint x\nhy : IsSelfAdjoint y\n⊢ IsSelfAdjoint (x / y)",
"tactic": "simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]"
}
] | [
258,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
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