file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/CategoryTheory/Endomorphism.lean | CategoryTheory.End.smul_right | [] | [
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Mathlib/LinearAlgebra/Projection.lean | Submodule.coe_isComplEquivProj_symm_apply | [] | [
364,
77
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363,
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Mathlib/GroupTheory/Complement.lean | Subgroup.MemRightTransversals.toEquiv_apply | [
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410,
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_pow | [
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70
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Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str | [
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"tactic": "rw [← Adjunction.homEquiv_naturality_right, ←... | [
459,
90
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | Complex.exp_eq_exp_ℂ | [
{
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},
{
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226,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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Mathlib/Data/Fintype/Card.lean | Fintype.card_eq | [] | [
212,
29
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208,
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Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.ofEquiv | [
{
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Mathlib/Topology/Sequences.lean | IsSeqCompact.subseq_of_frequently_in | [] | [
273,
34
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268,
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.tendsto_add_haar_inter_smul_one_of_density_one_aux | [
{
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804,
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755,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.zero_mod | [
{
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] | [
1044,
99
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Mathlib/Data/Finset/Lattice.lean | Finset.iSup_union | [
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Mathlib/Analysis/Convex/Slope.lean | ConvexOn.strict_mono_of_lt | [
{
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365,
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350,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.centralizer_eq_top_iff_subset | [] | [
1416,
59
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1415,
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Mathlib/Data/MvPolynomial/Expand.lean | MvPolynomial.expand_monomial | [] | [
55,
23
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53,
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.biUnion_decode₂ | [] | [
157,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Data/Finset/PImage.lean | Part.toFinset_some | [
{
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18
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_div | [
{
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] | [
73,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GradedMonoid.lean | SetLike.homogeneous_coe | [] | [
686,
14
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685,
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Mathlib/Data/PNat/Prime.lean | PNat.Prime.one_lt | [] | [
122,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/Topology/MetricSpace/CantorScheme.lean | CantorScheme.Disjoint.map_injective | [
{
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117,
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Ico.coe_eq_zero | [
{
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204,
24
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.r_eq_r' | [
{
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"sta... | [
198,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub | [
{
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.dirac_prod_dirac | [
{
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Mathlib/Data/Matrix/Basic.lean | Matrix.updateColumn_apply | [
{
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.get?_tail | [] | [
279,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
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Mathlib/Topology/StoneCech.lean | stoneCechExtend_extends | [] | [
280,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.eq_union_right | [
{
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}
] | [
1835,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Basic.lean | Complex.abs_re_le_abs | [
{
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{
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1033,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_one | [] | [
285,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
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Mathlib/Order/Hom/Lattice.lean | InfHom.id_apply | [] | [
582,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_diff | [
{
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113,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.isHaarMeasure_eq_smul_isHaarMeasure | [
{
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.mono | [] | [
346,
47
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343,
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.Preadditive.exact_of_iso_of_exact' | [] | [
120,
100
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116,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.IsLimit.ne_zero | [] | [
840,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
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Mathlib/Init/Data/Bool/Lemmas.lean | Bool.decide_congr | [
{
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{
... | [
159,
57
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.mul_apply' | [] | [
1113,
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1112,
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.mem_toPrepartition | [] | [
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96
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Mathlib/Order/Filter/Interval.lean | Filter.Tendsto.Ioc | [] | [
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71
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84,
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Std/Data/Int/DivMod.lean | Int.dvd_natAbs | [
{
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{
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] | [
659,
41
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Mathlib/Data/Real/Irrational.lean | Irrational.ne_zero | [
{
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175,
75
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175,
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Mathlib/Data/Finset/Image.lean | Finset.image_biUnion | [
{
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.pow_of_dvd | [
{
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Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.IsCompactElement.directed_sSup_lt_of_lt | [
{
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.const_smul_left | [] | [
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Mathlib/Algebra/Order/Field/Pi.lean | Pi.exists_forall_pos_add_lt | [
{
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_univ_single | [
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Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.smul_swap | [] | [
73,
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Mathlib/Order/WellFoundedSet.lean | Set.wellFoundedOn_empty | [] | [
65,
27
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Mathlib/Probability/Integration.lean | ProbabilityTheory.IndepFun.integral_mul' | [] | [
301,
25
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Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀' | [
{
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117,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.compMeasurable_mk | [] | [
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248,
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Mathlib/CategoryTheory/Category/TwoP.lean | TwoP.swapEquiv_symm | [] | [
106,
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105,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_uIcc_right | [
{
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306,
44
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.characteristic_iff_map_le | [
{
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Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.eq_curry_iff | [] | [
220,
54
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219,
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_of_mul_lt_mul_left' | [] | [
133,
31
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130,
1
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Mathlib/GroupTheory/OrderOfElement.lean | finEquivPowers_apply | [] | [
749,
6
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747,
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Mathlib/Order/WithBot.lean | WithBot.toDual_lt_toDual_iff | [] | [
1024,
10
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1023,
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Mathlib/Algebra/Quaternion.lean | Quaternion.self_add_star' | [] | [
1109,
19
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1108,
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.bicone_ι | [] | [
406,
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405,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_lt_iff_of_compact | [
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Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_symm | [] | [
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17
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_comp_val_Iio_atBot | [
{
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Mathlib/Data/Set/Sigma.lean | Set.sigma_preimage_left | [] | [
167,
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Mathlib/Topology/DenseEmbedding.lean | DenseInducing.closure_image_mem_nhds | [
{
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Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.t2Space | [
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Mathlib/Analysis/Calculus/FDeriv/Linear.lean | IsBoundedLinearMap.hasFDerivAtFilter | [] | [
112,
44
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Mathlib/Order/UpperLower/Basic.lean | ordConnected_iff_upperClosure_inter_lowerClosure | [
{
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_left_cancel | [
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] | [
119,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Field/Basic.lean | inv_sub_inv' | [
{
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] | [
178,
78
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Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.t'_jii | [
{
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Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.eval_part | [
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1164,
40
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Std/Data/Rat/Lemmas.lean | Rat.divInt_self | [
{
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122,
87
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.comp_affineMap | [
{
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Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Functor.rightAdjoint_of_isEquivalence | [] | [
659,
6
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658,
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Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.C_half_mul_two_eq_one | [
{
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154,
39
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153,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupNorm.coe_sup | [] | [
958,
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Mathlib/Data/Set/Prod.lean | Set.univ_pi_update | [
{
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source_aux | [
{
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Mathlib/Data/Nat/PartENat.lean | PartENat.natCast_ne_top | [] | [
358,
30
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.pentagon | [
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Mathlib/Data/List/Perm.lean | List.permutations'Aux_nthLe_zero | [
{
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_le_lsub | [] | [
1609,
35
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1608,
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Mathlib/Data/Int/Bitwise.lean | Int.land_bit | [
{
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}
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34
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314,
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Mathlib/Topology/Algebra/Group/Basic.lean | singleton_mul_mem_nhds | [
{
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Mathlib/Algebra/CharP/Basic.lean | CharP.ringChar_ne_zero_of_finite | [] | [
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40
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1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.exists_eval₂_eq_zero | [] | [
118,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeries_of_derivedLength_succ | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI✝ J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nI : LieIdeal R L\nk : ℕ\n⊢ derivedLengthOfIdeal R L I = k + 1 ↔ derivedSeriesOfIdeal R L (k + 1... | [
323,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_pos | [
{
"state_after": "no goals",
"state_before": "b o : Ordinal\nhb : 1 < b\nho : o ≠ 0\nhbo : b ≤ o\n⊢ 0 < log b o",
"tactic": "rwa [← succ_le_iff, succ_zero, ← opow_le_iff_le_log hb ho, opow_one]"
}
] | [
344,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition | [] | [
442,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.IsPushout.isVanKampen_iff | [
{
"state_after": "case mp\nJ : Type v'\ninst✝¹ : Category J\nC : Type u\ninst✝ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\nH : IsPushout f g h i\n⊢ IsVanKampen H → IsVanKampenColimit (PushoutCocone.mk h i (_ : f ≫ h = g ≫ i))\n\ncase mpr\nJ : Type v'\ninst✝¹ : Category J\nC : Type u\n... | [
118,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def | [] | [
344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.sMod_nonneg | [
{
"state_after": "case zero\np : ℕ\nw : 0 < p\n⊢ 0 ≤ 4 % (2 ^ p - 1)\n\ncase succ\np : ℕ\nw : 0 < p\nn✝ : ℕ\n⊢ 0 ≤ (sMod p n✝ ^ 2 - 2) % (2 ^ p - 1)",
"state_before": "p : ℕ\nw : 0 < p\ni : ℕ\n⊢ 0 ≤ sMod p i",
"tactic": "cases i <;> dsimp [sMod]"
},
{
"state_after": "no goals",
"state_before... | [
111,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.zsmul_f_apply | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Involutive.leftInverse | [] | [
890,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
11
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mul_comp | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.coe_bit1 | [] | [
573,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
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