file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_eq_zero'' | [] | [
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WSameSide.trans_sOppSide | [] | [
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_δ' | [
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_zero | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_card_le | [] | [
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C | [
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Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_sInf_rng | [
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Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_def | [] | [
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Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.id_apply_of_ne | [
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145,
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Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingSeminorm.seminorm_one_eq_one_iff_ne_zero | [
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152,
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Std/Data/HashMap/WF.lean | Std.HashMap.Imp.pairwise_replaceF | [
{
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219,
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.SMul.aux_of | [] | [
205,
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Mathlib/Data/Nat/Basic.lean | Nat.div_eq_iff_eq_mul_left | [
{
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665,
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662,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.diff_null_ae_eq_self | [] | [
480,
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Mathlib/RingTheory/Polynomial/Tower.lean | Polynomial.aeval_algebraMap_eq_zero_iff_of_injective | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_X_pow | [
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.coe_ideal_span_singleton_div_self | [
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Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.comp_nullHomotopicMap | [
{
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.rfl | [] | [
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Mathlib/Algebra/Periodic.lean | Function.Periodic.mul_const' | [
{
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149,
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_inv_fst | [
{
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Mathlib/Algebra/Star/Subalgebra.lean | Set.star_mem_centralizer | [
{
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Mathlib/Topology/Separation.lean | pure_le_nhds_iff | [] | [
545,
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544,
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Mathlib/Init/Algebra/Order.lean | le_of_eq_or_lt | [] | [
165,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
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Mathlib/Init/Logic.lean | true_or_iff | [] | [
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179,
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Mathlib/Data/Set/Function.lean | Set.LeftInvOn.comp | [] | [
1065,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
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Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.congr_fun | [] | [
274,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.lt_opow_iff_log_lt | [] | [
340,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
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Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_eq_zero | [
{
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{
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156,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_antiperiodic | [
{
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}
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307,
76
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Mathlib/Topology/Basic.lean | acc_principal_iff_cluster | [
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1177,
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Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean | SubMulAction.coe_mul | [] | [
66,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_antiperiodic | [
{
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.add_mem_iff_right | [] | [
571,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Support.lean | Function.support_const_smul_of_ne_zero | [
{
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_X | [] | [
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Mathlib/LinearAlgebra/FreeModule/Basic.lean | Module.Free.of_equiv | [] | [
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38
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Mathlib/Data/Set/Function.lean | Set.surjOn_iff_exists_bijOn_subset | [
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Mathlib/Data/Prod/TProd.lean | List.TProd.elim_of_mem | [
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Mathlib/Order/Filter/Basic.lean | Filter.frequently_false | [
{
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_Union | [] | [
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15
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.gen_eq_preimage_restrict | [
{
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_mul | [
{
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Mathlib/Data/Fin/VecNotation.lean | Matrix.head_add | [] | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_sup | [
{
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657,
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Mathlib/Algebra/GeomSum.lean | geom_sum_neg_iff | [
{
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574,
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Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.map_succ' | [] | [
136,
13
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135,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.inner_right_fintype | [
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Mathlib/Data/Sum/Basic.lean | Sum.elim_const_const | [
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626,
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Mathlib/Data/Set/Function.lean | Set.mapsTo_iff_exists_map_subtype | [
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382,
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379,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.det_to_matrix_orthonormalBasis | [
{
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711,
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706,
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Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.mkDerivation_monomial | [] | [
157,
31
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154,
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Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_add | [] | [
83,
42
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81,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPushout_symmetry | [] | [
1553,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1551,
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | ContDiff.arsinh | [] | [
286,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
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Mathlib/Topology/Semicontinuous.lean | upperSemicontinuous_biInf | [] | [
1064,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
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Mathlib/Data/Set/Function.lean | Function.Injective.comp_injOn | [] | [
1596,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
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Mathlib/Data/List/Indexes.lean | List.new_def_eq_old_def | [
{
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{
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146,
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140,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.deriv_arctan | [] | [
107,
46
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106,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.right_le_sup | [
{
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365,
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Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_add_right_right | [
{
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320,
32
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318,
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Mathlib/Topology/Separation.lean | normalOfCompactT2 | [] | [
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79
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1732,
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.compl | [] | [
1578,
17
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1576,
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasFDerivAt_exp_smul_const_of_mem_ball | [
{
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305,
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Mathlib/Order/Hom/Basic.lean | OrderIso.symm_symm | [
{
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881,
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879,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousCore'_le | [] | [
127,
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126,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mem_graph | [
{
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737,
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.liftOn₂_mk | [] | [
401,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
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Mathlib/Data/Nat/PartENat.lean | PartENat.lt_add_iff_pos_right | [
{
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{
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482,
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480,
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Std/Data/List/Init/Lemmas.lean | List.reverse_concat | [
{
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{
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157,
45
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156,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_subset_iff | [] | [
702,
20
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701,
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Std/Data/List/Lemmas.lean | List.infix_cons_iff | [
{
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1700,
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1691,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.map_vadd | [] | [
136,
29
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135,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_subset_iff | [] | [
1531,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
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Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.yonedaEvaluation_map_down | [] | [
318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.le_iff_eq | [] | [
487,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
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Mathlib/Topology/Maps.lean | isClosedMap_iff_closure_image | [
{
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537,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_comp | [] | [
1147,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
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Mathlib/RingTheory/SimpleModule.lean | LinearMap.bijective_of_ne_zero | [] | [
165,
41
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163,
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Mathlib/Algebra/GradedMonoid.lean | SetLike.coe_gnpow | [] | [
620,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
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Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.pow_dichotomy | [
{
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530,
34
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525,
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Mathlib/MeasureTheory/Function/EssSup.lean | ENNReal.ae_le_essSup | [] | [
310,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_empty | [] | [
346,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
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Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_smul | [] | [
501,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
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Mathlib/Order/Hom/Basic.lean | OrderIso.complementedLattice | [
{
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1376,
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Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_algEquiv_lpBcf_symm | [] | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.snorm_exponent_top_lim_le_liminf_snorm_exponent_top | [
{
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69
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1206,
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Mathlib/Combinatorics/Additive/Energy.lean | Finset.multiplicativeEnergy_mono_left | [] | [
63,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
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Mathlib/Order/Heyting/Basic.lean | inf_himp_le | [
{
"state_after": "no goals",
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"tactic": "rw [inf_comm, ← le_himp_iff]"
}
] | [
350,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
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Mathlib/Data/TwoPointing.lean | TwoPointing.prop_snd | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.compl | [] | [
436,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
11
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Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.mk_associator_hom | [] | [
280,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
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Mathlib/Data/Set/Image.lean | Set.rangeSplitting_injective | [] | [
1170,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1169,
1
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toLinearMap_injective | [] | [
169,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_mul_of_coprime | [
{
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1751,
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Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.comm | [] | [
45,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_erase_lt | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.561231\nhp : p ≠ 0\n⊢ degree (erase (natDegree p) p) ≠ degree p",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.561231\nhp : p ≠ 0\n⊢ degre... | [
744,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.dvd_prime | [] | [
204,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mem_map | [
{
"state_after": "M : Type u_1\nN : Type u_2\nP : Type ?u.13819\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : MulOneClass P\nS✝ : Submonoid M\nF : Type u_3\nmc : MonoidHomClass F M N\nf : F\nS : Submonoid M\ny : N\n⊢ y ∈ map f S ↔ ∃ x x_1, ↑f x = y",
"state_before": "M : Type u_1\nN : Type u_2\nP... | [
239,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_union_inter | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.17454\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns : Finset α\na : α\ninst✝ : DecidableEq α\ns₁ s₂ : Finset α\nb₁ b₂ : β\n⊢ op (Multiset.fold op b₁ (Multiset.map f (s₁ ∪ s₂).val)) (Multiset.fold op b₂ (Multiset.m... | [
119,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
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