file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_le_comap_of_inv_on | [
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.hasCoequalizers_of_hasColimit_parallelPair | [] | [
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Mathlib/Algebra/GroupPower/Basic.lean | zpow_neg_coe_of_pos | [] | [
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Mathlib/Order/Hom/Bounded.lean | BotHom.symm_dual_comp | [] | [
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Mathlib/Analysis/Normed/Group/Basic.lean | eq_of_norm_div_le_zero | [
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2002,
43
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2001,
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Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.union | [] | [
106,
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_pos | [
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Mathlib/Order/Filter/Bases.lean | Set.PairwiseDisjoint.exists_mem_filter_basis | [
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Mathlib/Data/Real/Pi/Leibniz.lean | Real.tendsto_sum_pi_div_four | [
{
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"state_before": "⊢ Tendsto (fun k => ∑ i in Finset.range k, (-1) ^ i / (2 * ↑i + 1)) atTop (𝓝 (π / 4))",
"tactic": "rw [tendsto_iff_norm_tendsto_zero, ← tendsto_zero_iff_norm_tendsto_zero]"
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139,
92
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots' | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.succ_lt_of_isLimit | [] | [
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Mathlib/LinearAlgebra/Dual.lean | Submodule.dualAnnihilator_dualCoannihilator_dualAnnihilator | [] | [
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivCongrLeft_apply | [] | [
369,
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Mathlib/Data/Nat/Prime.lean | Nat.Prime.pred_pos | [] | [
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Std/Data/Int/DivMod.lean | Int.fdiv_eq_ediv | [
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Mathlib/Data/Sum/Basic.lean | Sum.getLeft_eq_none_iff | [
{
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Mathlib/Data/Finset/Sups.lean | Finset.image_subset_sups_left | [] | [
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27
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_pow_apply_head | [
{
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340,
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.left_mem_Ico | [] | [
122,
22
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.continuous_normSq | [] | [
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74
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1024,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.coe_add | [] | [
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68
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.setOf_sSameSide_eq_image2 | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.zpow_le_of_le | [
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.div_C_mul | [
{
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Mathlib/Data/Quot.lean | Quotient.liftOn₂'_mk'' | [] | [
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurableSet_inl_image | [
{
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Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_finset_image | [] | [
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Mathlib/Data/List/Lattice.lean | List.union_sublist_append | [] | [
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Mathlib/Algebra/Ring/Defs.lean | one_sub_mul | [
{
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] | [
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Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.trans | [] | [
111,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftRingHom_apply_div | [] | [
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897,
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Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.mul_assoc | [
{
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Mathlib/Data/Complex/Exponential.lean | Complex.two_cosh | [] | [
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Mathlib/Algebra/Squarefree.lean | multiplicity.squarefree_iff_multiplicity_le_one | [
{
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Mathlib/Algebra/BigOperators/Order.lean | Finset.single_le_prod' | [] | [
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Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndinter_subset_left | [] | [
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Mathlib/Data/Complex/Basic.lean | Complex.conj_bit1 | [
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Mathlib/RingTheory/Filtration.lean | Ideal.mem_iInf_smul_pow_eq_bot_iff | [
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Mathlib/LinearAlgebra/Dual.lean | Module.eval_apply_eq_zero_iff | [
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Mathlib/Algebra/Group/Basic.lean | mul_rotate | [
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Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_mul_right | [
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_mk'_spec | [] | [
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_mul_mk'_of_map_mul | [
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Real.contDiff_exp | [] | [
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Mathlib/Analysis/NormedSpace/IndicatorFunction.lean | norm_indicator_le_of_subset | [
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.support_smul_eq | [
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1565,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.resolvent_eq | [] | [
149,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_tensor_id | [
{
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505,
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498,
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.transpose_eq_iff | [
{
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{
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237,
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235,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mapLe_isCycle | [] | [
1629,
53
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1627,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.pred_succ | [
{
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175,
88
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173,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.cauchySeq_iff' | [] | [
749,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
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Std/Data/Int/DivMod.lean | Int.emod_add_ediv' | [
{
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{
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] | [
399,
41
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398,
1
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Mathlib/Data/List/TFAE.lean | List.tfae_of_cycle | [
{
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67,
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Mathlib/LinearAlgebra/Dimension.lean | rank_add_rank_split | [
{
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1137,
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1110,
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Mathlib/Algebra/GroupWithZero/Defs.lean | mul_right_injective₀ | [] | [
70,
33
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.comp_aeval | [
{
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Mathlib/MeasureTheory/Function/L2Space.lean | integral_eq_zero_of_forall_integral_inner_eq_zero | [
{
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112,
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Mathlib/Analysis/NormedSpace/Star/Basic.lean | IsSelfAdjoint.nnnorm_pow_two_pow | [
{
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275,
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269,
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Mathlib/LinearAlgebra/Ray.lean | sameRay_neg_smul_left_iff_of_ne | [] | [
574,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
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Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_def | [] | [
152,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Logic/Basic.lean | xor_not_left | [
{
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}
] | [
296,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
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Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.alg_hom_ext' | [] | [
220,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mem_lieSpan | [
{
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681,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.sub_mem | [] | [
668,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
11
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Filter.Tendsto.isBoundedUnder_le | [] | [
45,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_mono_ae | [] | [
311,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.kernelForkOfFork_ι | [] | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_conj | [
{
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124,
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121,
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Mathlib/Topology/Instances/Matrix.lean | Matrix.diagonal_tsum | [
{
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366,
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360,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.norm_Integral_le_one | [
{
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586,
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_add_supp | [
{
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74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
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Mathlib/Algebra/Quaternion.lean | Quaternion.re_add_im | [] | [
820,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
16
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Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean | is_ideal_adic_pow | [
{
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208,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
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Mathlib/CategoryTheory/Functor/Flat.lean | CategoryTheory.flat_of_preservesFiniteLimits | [
{
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198,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.ceil_lt_mul | [
{
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"tactic": "refine' (ceil_lt_add_one <| ... | [
367,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.concatRec_nil | [] | [
464,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
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Mathlib/Data/List/Sigma.lean | List.head?_lookupAll | [
{
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"tactic": "simp"
},
{
"state_after": "case pos\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α... | [
289,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_neg | [] | [
778,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
11
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Mathlib/Algebra/BigOperators/Basic.lean | MonoidHom.coe_finset_prod | [] | [
279,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.log_stirlingSeq_diff_hasSum | [
{
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105,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_eq_inter_edgeSet | [
{
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1164,
54
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1161,
1
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.paste_horiz_iff | [] | [
763,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.U_real_cos | [
{
"state_after": "no goals",
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"tactic": "exact_mod_cast U_complex_cos θ n"
}
] | [
126,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.mul_subset_iff_left | [] | [
432,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
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Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_ne_zero_of_isUnit_det | [
{
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303,
24
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294,
1
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Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.isVonNBounded_iff_smul_tendsto_zero | [
{
"state_after": "no goals",
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193,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/Geometry/Manifold/ChartedSpace.lean | achart_val | [] | [
573,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
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src/lean/Init/Core.lean | And.comm | [
{
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"tactic": "constructor <;> intro ⟨h₁, h₂⟩ <;> exact ⟨h₂, h₁⟩"
}
] | [
681,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
680,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.93631\nα : Type u_1\nβ : Type ?u.93637\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a \\ b = ⊥ ↔ a ≤ b",
"tactic": "rw [← le_bot_iff, sdiff_le_iff, sup_bot_eq]"
}
] | [
596,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.comp_assoc | [] | [
319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_sq_mul_cos | [
{
"state_after": "a b : ℝ\nn : ℕ\nthis : (∫ (x : ℝ) in a..b, sin x ^ 2 * cos x ^ (2 * 0 + 1)) = ∫ (u : ℝ) in sin a..sin b, u ^ 2 * (1 - u ^ 2) ^ 0\n⊢ (∫ (x : ℝ) in a..b, sin x ^ 2 * cos x) = (sin b ^ 3 - sin a ^ 3) / 3",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x ^ 2 * cos x) = (sin b ^ 3 ... | [
776,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.ext_iff' | [] | [
190,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.snd_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.5372563\nβ : Type u_1\nβ' : Type ?u.5372569\nγ : Type ?u.5372572\nE : Type ?u.5372575\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' :... | [
843,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.exist_integer_multiples | [
{
"state_after": "R : Type u_2\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_3\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.23842\ninst✝¹ : CommRing P\ninst✝ : IsLocalization M S\nι : Type u_1\ns : Finset ι\nf : ι → S\nthis : (a : Prop) → Decidable a\n⊢ ∃ b, ∀ (i : ι), i ∈ s → IsInteger R (↑b • f... | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_neg | [
{
"state_after": "case inl\nr : ℝ\nhn : r < 0\n⊢ sign (-r) = -sign r\n\ncase inr.inl\n\n⊢ sign (-0) = -sign 0\n\ncase inr.inr\nr : ℝ\nhp : 0 < r\n⊢ sign (-r) = -sign r",
"state_before": "r : ℝ\n⊢ sign (-r) = -sign r",
"tactic": "obtain hn | rfl | hp := lt_trichotomy r (0 : ℝ)"
},
{
"state_after"... | [
89,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_sub_pi | [] | [
885,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.copy_eq | [] | [
714,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_finset_sup_eq_iInter | [
{
"state_after": "case intro\nR : Type ?u.1073638\nR' : Type ?u.1073641\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1073647\n𝕜₃ : Type ?u.1073650\n𝕝 : Type ?u.1073653\nE : Type u_2\nE₂ : Type ?u.1073659\nE₃ : Type ?u.1073662\nF : Type ?u.1073665\nG : Type ?u.1073668\nι : Type u_3\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : AddCo... | [
860,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.HasBasis.equicontinuousAt_iff_left | [
{
"state_after": "ι : Type u_3\nκ✝ : Type ?u.121547\nX : Type u_2\nY : Type ?u.121553\nZ : Type ?u.121556\nα : Type u_4\nβ : Type ?u.121562\nγ : Type ?u.121565\n𝓕 : Type ?u.121568\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSp... | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
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