file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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src/lean/Init/Data/Nat/Div.lean | Nat.mod.inductionOn | [] | [
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivWithinAt_fst | [] | [
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Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulLeft_toAddMonoidHom | [] | [
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Mathlib/Algebra/Order/Floor.lean | Int.floor_nonpos | [
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Mathlib/Topology/LocallyFinite.lean | locallyFinite_option | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_nil | [] | [
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.zero_add | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.fg_bot | [
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Functor.asEquivalence_unit | [] | [
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Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean | SubMulAction.mem_mul | [] | [
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14
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Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Cotrident.condition | [
{
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28
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Mathlib/Data/Bool/Basic.lean | Bool.xor_false_right | [
{
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Mathlib/Topology/MetricSpace/Basic.lean | dist_pi_le_iff | [
{
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.isCauSeq_im | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mod_def | [] | [
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.addHaarMeasure_eq_volume | [
{
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{
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Mathlib/Data/Finset/Basic.lean | Finset.Subset.trans | [] | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.attach_affineCombination_of_injective | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.mul_isBigO | [
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Mathlib/Data/Set/Image.lean | Function.LeftInverse.preimage_preimage | [
{
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Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eq_zero_on_vertical_strip | [] | [
324,
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Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.bisim_lemma | [
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Mathlib/Data/Finset/Basic.lean | Finset.exists_of_ssubset | [] | [
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Mathlib/MeasureTheory/CardMeasurableSpace.lean | MeasurableSpace.cardinal_generateMeasurableRec_le | [
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.irreducible_of_degree_eq_one | [] | [
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43
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_C_mul | [
{
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Mathlib/Data/Set/Image.lean | Subtype.preimage_coe_compl' | [] | [
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.single_apply | [] | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_diff_Ico_same | [
{
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Mathlib/Order/Hom/Bounded.lean | TopHom.id_comp | [] | [
283,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
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Std/Control/ForInStep/Lemmas.lean | ForInStep.run_yield | [] | [
18,
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | Set.Finite.nullMeasurableSet | [] | [
366,
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365,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_ofReal_re | [] | [
587,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
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Mathlib/Data/Num/Lemmas.lean | ZNum.bit1_of_bit1 | [
{
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},
{
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1125,
97
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1122,
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Mathlib/GroupTheory/Complement.lean | Subgroup.mem_leftTransversals_iff_bijective | [] | [
267,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
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Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.continuousLinearEquivOfBilin_apply | [] | [
123,
41
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121,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_strictMono_of_surjective | [] | [
655,
31
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654,
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.IsNClique.mono | [
{
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121,
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119,
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Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.cancel_left | [
{
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.min | [
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Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.Paths.lift_nil | [] | [
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54
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.map_zero | [] | [
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Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.uniformContinuous_coe | [] | [
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_mem_iff | [
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.neg_apply | [] | [
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Mathlib/Data/Rat/Defs.lean | Rat.divInt_eq_div | [
{
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Mathlib/LinearAlgebra/Finrank.lean | Subalgebra.finrank_toSubmodule | [] | [
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Mathlib/Algebra/Associated.lean | comap_prime | [
{
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Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulDysonEtransform.card | [
{
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73,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
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Mathlib/Analysis/Complex/OperatorNorm.lean | Complex.conjCle_norm | [] | [
68,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_singleton | [] | [
370,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerTMul_assoc | [] | [
519,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.inverse_apply_eq | [
{
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1056,
35
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1049,
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Mathlib/Topology/VectorBundle/Basic.lean | Pretrivialization.linearMapAt_symmₗ | [
{
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163,
45
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160,
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Mathlib/Data/Polynomial/Div.lean | Polynomial.rootMultiplicity_eq_zero | [] | [
569,
55
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568,
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | map_le_lineMap_iff_slope_le_slope | [
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281,
77
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278,
1
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Std/Data/String/Lemmas.lean | String.utf8GetAux_of_valid | [
{
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208,
49
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199,
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.pow_log_eq_self | [] | [
476,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
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Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_div_mul_le_card_mul_mul_card_mul | [
{
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67,
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64,
1
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_toAddSubgroup | [] | [
1477,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1475,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_iUnion | [
{
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226,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbent.absorbs | [] | [
141,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/Topology/Inseparable.lean | SeparationQuotient.map_prod_map_mk_nhds | [
{
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516,
83
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515,
1
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toLinearEquiv_refl | [] | [
549,
6
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548,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | isComplete_iUnion_separated | [
{
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364,
40
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346,
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Mathlib/Data/Set/Finite.lean | Set.Finite.insert | [
{
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},
{
... | [
849,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
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Mathlib/Analysis/Calculus/Deriv/Pow.lean | deriv_pow' | [] | [
96,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | map_le_lineMap_iff_slope_le_slope_left | [
{
"state_after": "no goals",
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217,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/LinearAlgebra/QuotientPi.lean | Submodule.quotientPi_aux.left_inv | [
{
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103,
29
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98,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.trans_isBigO | [] | [
493,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
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Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.toMatrix_self | [
{
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54,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Data/Finset/Card.lean | Finset.eq_of_subset_of_card_le | [] | [
267,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Mathlib/Data/Prod/Basic.lean | Prod.map_map | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Data/List/Join.lean | List.join_join | [
{
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}
] | [
69,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_rpow_of_exponent_gt | [
{
"state_after": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x < 1\nhyz : z < y\n⊢ exp (log x * y) < exp (log x * z)",
"state_before": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x < 1\nhyz : z < y\n⊢ x ^ y < x ^ z",
"tactic": "repeat' rw [rpow_def_of_pos hx0]"
},
{
"state_after": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x < 1\nhy... | [
494,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.one_coeff_eq_of_pos | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\nhn : 0 < n\n⊢ ↑(aeval (Function.uncurry fun i => ![].coeff)) (wittOne p n) = 0",
"tactic": "simp only [hn, wittOne_pos_eq_zero, AlgHom.map_zero]"
}
] | [
347,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | finiteDimensional_direction_affineSpan_of_finite | [] | [
66,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Category/Mon/FilteredColimits.lean | MonCat.FilteredColimits.M.mk_eq | [] | [
77,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.mem_nhds | [] | [
176,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_toPath_subset | [] | [
1433,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1432,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.Exact.unop | [
{
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314,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | inf_sSup_eq | [] | [
94,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_of_eq | [] | [
351,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
11
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.coe_pointwise_smul | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.hasDerivAt_sin | [] | [
584,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.ofRankEqZero_apply | [] | [
1183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.Nonempty.pairwise_eq_iff_exists_eq | [] | [
121,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.I_zpow_bit0 | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ I ^ bit0 n = (-1) ^ n",
"tactic": "rw [zpow_bit0', I_mul_I]"
}
] | [
771,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup₂_le_iff | [
{
"state_after": "no goals",
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913,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.edist_ne_top | [] | [
47,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Mathlib/Init/Algebra/Classes.lean | asymm | [] | [
273,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.coe_sSup' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4651\nγ : Type ?u.4654\nι : Sort ?u.4657\ninst✝¹ : Preorder α\ninst✝ : SupSet α\ns : Set α\nhs : BddAbove s\n⊢ ↑(sSup s) =\n if ⊤ ∈ (fun a => ↑a) '' s then ⊤\n else\n if BddAbove ((fun a => ↑a) ⁻¹' ((fun a => ↑a) '' s)) then ↑(sSup ((fun a => ↑a) ⁻¹' ((fun ... | [
117,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.hsum_embDomain | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\nα : Type u_4\nβ : Type u_3\ns : SummableFamily Γ R α\nf : α ↪ β\na : α\nb : β\ng : Γ\n⊢ coeff (hsum (embDomain s f)) g = coeff (hsum s) g",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : Part... | [
1746,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1743,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMonoOn.cmp_map_eq | [] | [
942,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | LiouvilleNumber.remainder_summable | [
{
"state_after": "no goals",
"state_before": "m : ℝ\nhm : 1 < m\nk : ℕ\n⊢ Summable fun i => 1 / m ^ (i + (k + 1))!",
"tactic": "convert(summable_nat_add_iff (k + 1)).2 (LiouvilleNumber.summable hm)"
}
] | [
89,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.surjOn_iInter | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.193360\nι : Sort u_1\nι' : Sort ?u.193366\nι₂ : Sort ?u.193369\nκ : ι → Sort ?u.193374\nκ₁ : ι → Sort ?u.193379\nκ₂ : ι → Sort ?u.193384\nκ' : ι' → Sort ?u.193389\ninst✝ : Nonempty ι\ns : ι → Set α\nt : Set β\nf : α → β\nH : ∀ (i : ι), SurjOn f (s i) t\n... | [
1612,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1608,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_nonneg_of_ae_restrict | [] | [
727,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Data/Finmap.lean | Finmap.dlookup_list_toFinmap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : List (Sigma β)\n⊢ lookup a (List.toFinmap s) = dlookup a s",
"tactic": "rw [List.toFinmap, lookup_toFinmap, lookup_to_alist]"
}
] | [
277,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_ne_self | [] | [
1973,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1972,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_dvd_mul_right | [] | [
690,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
689,
11
] |
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