file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Data/Nat/Choose/Sum.lean | Finset.sum_antidiagonal_choose_succ_mul | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_erase_eq_div | [
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mk'_toAddSubmonoid | [] | [
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205,
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.cospherical_singleton | [
{
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{
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191,
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.fromLocalizedModule_mk | [] | [
777,
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.associated_pow_irreducible | [
{
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.zpow_apply | [] | [
240,
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_iUnion | [] | [
265,
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Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_add_le_tsub_right | [
{
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_sub | [
{
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] | [
229,
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Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivWithinAt_off_countable_of_le | [
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Mathlib/Algebra/Order/Archimedean.lean | exists_pow_lt_of_lt_one | [
{
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Std/Data/String/Lemmas.lean | String.data_singleton | [] | [
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76
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_singleton_eq_range | [
{
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1304,
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Mathlib/Data/Part.lean | Part.one_mem_one | [] | [
713,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonnegg_cases_left | [] | [
515,
44
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Mathlib/Order/Monotone/Union.lean | AntitoneOn.union_right | [] | [
120,
61
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Mathlib/Deprecated/Subfield.lean | Field.mem_closure | [] | [
129,
45
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128,
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.nat_coe_fst | [] | [
276,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.extension_iff_amalgamation | [
{
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.range_coe | [] | [
144,
27
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143,
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Mathlib/Analysis/Convex/Extreme.lean | mem_extremePoints_iff_forall_segment | [
{
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Mathlib/Order/Bounds/Basic.lean | le_isGLB_iff | [
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Mathlib/Data/Real/CauSeq.lean | CauSeq.mul_equiv_mul | [
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.hom_eq_inv | [
{
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{
"state... | [
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258,
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Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.comp_epiDesc | [] | [
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100
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Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | Finpartition.nonUniforms_bot | [
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Mathlib/GroupTheory/Submonoid/Center.lean | Submonoid.coe_center | [] | [
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Mathlib/Algebra/Parity.lean | Odd.strictMono_pow | [
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Mathlib/Data/Fintype/Card.lean | Fintype.one_lt_card | [] | [
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Std/Data/Int/Lemmas.lean | Int.toNat_one | [] | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | self_sub_toIocMod | [
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] | [
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32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_monomial | [
{
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Mathlib/Topology/TietzeExtension.lean | BoundedContinuousFunction.exists_extension_norm_eq_of_closedEmbedding' | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | innerₛₗ_apply_coe | [] | [
1757,
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Mathlib/Topology/Basic.lean | isClosed_compl_iff | [
{
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] | [
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Icc_iff_integrableOn_Ioo' | [
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Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_mul_right_add_right | [
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Mathlib/Algebra/Group/Basic.lean | eq_inv_mul_iff_mul_eq | [
{
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Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.lflip_apply | [] | [
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65
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Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.hasStrictInitial_of_isUniversal | [
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_apply | [] | [
1038,
49
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasFDerivAt_exp_smul_const | [] | [
384,
58
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Mathlib/Order/BoundedOrder.lean | eq_top_mono | [] | [
171,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.map_PInfty_f | [
{
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"state_before": "C : Type u_4\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\nX✝ : SimplicialObject C\nD : Type u_1\ninst✝² : Category D\ninst✝¹ : Preadditive D\nG : C ⥤ D\ninst✝ : Functor.Additive G\nX : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.Hom.f PInfty n = G.map (Homo... | [
200,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Order/Monotone/Basic.lean | Antitone.comp_monotoneOn | [] | [
671,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
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Mathlib/Algebra/RingQuot.lean | RingQuot.pow_quot | [
{
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"state_before": "R : Type u₁\ninst✝³ ... | [
250,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | summable_of_isEquivalent_nat | [] | [
706,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_mul_sub_add_iff | [] | [
435,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.add_left_cancel | [
{
"state_after": "no goals",
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"tactic": "induction n with\n| zero => simp; intros; assumption\n| succ n ih => simp [succ_add]; intro h; apply ih h"
},
{
"state_after": "case zero\nm k : Nat\n⊢ m = k → m = k",
"state_before": "case zero\n... | [
151,
54
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
148,
11
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.inv_map_inv_app | [
{
"state_after": "no goals",
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"tactic": "aesop_cat"
}
] | [
213,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/RepresentationTheory/Maschke.lean | LinearMap.conjugate_apply | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
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Mathlib/Topology/Constructions.lean | Continuous.comp₃ | [] | [
423,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.measure_iUnionNotConvergentSeq | [
{
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161,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isOrtho_def | [] | [
66,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Order/CompleteLattice.lean | iInf_range | [] | [
1388,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1387,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.map_one | [
{
"state_after": "no goals",
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"tactic": "rw [Filter.map_one', map_one, pure_one... | [
175,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
11
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.card_mul | [] | [
706,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
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Mathlib/Logic/Encodable/Basic.lean | nonempty_encodable | [] | [
476,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.ext | [] | [
605,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.toBlocks_fromBlocks₁₂ | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.map_prod | [
{
"state_after": "case empty\nR : Type u_2\nι : Type u_1\ninst✝ : CommMonoidWithZero R\ng : ι → ℕ\nf : ArithmeticFunction R\nhf : IsMultiplicative f\ns : Finset ι\nhs✝ : Set.Pairwise (↑s) (coprime on g)\nhs : Set.Pairwise (↑∅) (coprime on g)\n⊢ ↑f (∏ i in ∅, g i) = ∏ i in ∅, ↑f (g i)\n\ncase insert\nR : Type u_... | [
610,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
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Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.add | [] | [
108,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.localization_toBasicOpen | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nf g : R\n⊢ ↑(RingHom.comp (toBasicOpen R f) (algebraMap R (Localization.Away f))) g = ↑(toOpen R (PrimeSpectrum.basicOpen f)) g",
"tactic": "rw [toBasicOpen, IsLocalization.Away.lift, RingHom.comp_apply, IsLocalization.lift_eq... | [
639,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Computability/DFA.lean | DFA.eval_append_singleton | [] | [
89,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Topology/MetricSpace/Holder.lean | HolderWith.nndist_le | [] | [
251,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.ext | [] | [
237,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_div | [
{
"state_after": "case inl\nn : ℕ\nh : 0 ∣ n\n⊢ factorization (n / 0) = factorization n - factorization 0\n\ncase inr\nd n : ℕ\nh : d ∣ n\nhd : d ≠ 0\n⊢ factorization (n / d) = factorization n - factorization d",
"state_before": "d n : ℕ\nh : d ∣ n\n⊢ factorization (n / d) = factorization n - factorization ... | [
524,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.pre_map | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁶ : Category C\ninst✝⁵ : MonoidalCategory C\nA B X X' Y Y' Z : C\ninst✝⁴ : Closed A\ninst✝³ : Closed B\nA₁ A₂ A₃ : C\ninst✝² : Closed A₁\ninst✝¹ : Closed A₂\ninst✝ : Closed A₃\nf : A₁ ⟶ A₂\ng : A₂ ⟶ A₃\n⊢ pre (f ≫ g) = pre g ≫ pre f",
"tacti... | [
284,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Limit.π_mk | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nx : (j : J) → F.obj j\nh : ∀ (j j' : J) (f : j ⟶ j'), F.map f (x j) = x j'\nj : J\n⊢ limit.π F j\n (↑(limitEquivSections F).symm { val := x, property := (_ : ∀ {j j' : J} (f : j ⟶ j'), F.map f (x j) = x j') }) =\n x j",
"state_b... | [
147,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Homology/Additive.lean | CochainComplex.single₀MapHomologicalComplex_inv_app_succ | [] | [
448,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_nil | [] | [
740,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_int_mul_pi | [] | [
1031,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Topology/Maps.lean | Inducing.isClosedMap | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.226053\nδ : Type ?u.226056\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\nhf : Inducing f\nh : IsClosed (range f)\ns : Set α\nhs : IsClosed s\n⊢ IsClosed (f '' s)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.226053... | [
528,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit0_le_bit | [] | [
702,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.IsImage.lift_ι | [] | [
369,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.leftUnitor_naturality | [
{
"state_after": "case H\nR : Type u\ninst✝ : CommRing R\nM N : ModuleCat R\nf : M ⟶ N\n⊢ LinearMap.compr₂ (TensorProduct.mk R ↑(of R R) ↑M) (tensorHom (𝟙 (of R R)) f ≫ (leftUnitor N).hom) =\n LinearMap.compr₂ (TensorProduct.mk R ↑(of R R) ↑M) ((leftUnitor M).hom ≫ f)",
"state_before": "R : Type u\ninst... | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_le_add_left_neg | [
{
"state_after": "x : PGame\n⊢ -(-x + x) ≤ 0",
"state_before": "x : PGame\n⊢ 0 ≤ -x + x",
"tactic": "rw [← neg_le_neg_iff, neg_zero]"
},
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ -(-x + x) ≤ 0",
"tactic": "exact neg_add_le.trans (add_left_neg_le_zero _)"
}
] | [
1682,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Mathlib/Topology/Basic.lean | topologicalSpace_eq_iff | [
{
"state_after": "case a.h.a\nα : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\nt t' : TopologicalSpace α\nh : ∀ (s : Set α), IsOpen s ↔ IsOpen s\nx✝ : Set α\n⊢ IsOpen x✝ ↔ IsOpen x✝",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t✝ : Set α\np p₁ p₂ : ... | [
137,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.hasDerivAt_cosh | [] | [
660,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.span | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : IsFilteredOrEmpty C\ni j j' : C\nf : i ⟶ j\nf' : i ⟶ j'\nK : C\nG : j ⟶ K\nG' : j' ⟶ K\nh✝ : True\nk : C\ne : K ⟶ k\nhe : (f ≫ G) ≫ e = (f' ≫ G') ≫ e\n⊢ f ≫ G ≫ e = f' ≫ G' ≫ e",
"tactic": "simpa only [← Category.asso... | [
411,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.isLUB_norm | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : Nonempty α\nf : { x // x ∈ lp E ⊤ }\n⊢ IsLUB (Set.range fun i => ‖↑f i‖) (⨆ (i : α), ‖↑f i‖)",
"state_before": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup... | [
406,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Topology/Separation.lean | t1Space_antitone | [] | [
557,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.multiset_sum_mem | [] | [
391,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_univ | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.83299\n𝕜 : Type ?u.83302\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\ns : Set (Sym2 V)\nv w : V\n⊢ Adj (fromEdgeSet Set.univ) v w ↔ Adj ⊤ v w",
"state_before": "ι : Sort ?u.83299\n𝕜 : Type ?u.83302\... | [
645,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Order/Ideal.lean | Order.Cofinal.above_mem | [] | [
541,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Data/List/Rotate.lean | List.IsRotated.cyclicPermutations | [
{
"state_after": "case intro\nα : Type u\nl✝ l' l : List α\nk : ℕ\n⊢ List.cyclicPermutations l ~r List.cyclicPermutations (rotate l k)",
"state_before": "α : Type u\nl✝ l'✝ l l' : List α\nh : l ~r l'\n⊢ List.cyclicPermutations l ~r List.cyclicPermutations l'",
"tactic": "obtain ⟨k, rfl⟩ := h"
},
{
... | [
686,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_symm_coe_above | [] | [
189,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_smul_closedBall | [
{
"state_after": "R : Type ?u.1129059\nR' : Type ?u.1129062\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1129068\n𝕜₃ : Type ?u.1129071\n𝕝 : Type ?u.1129074\nE : Type u_2\nE₂ : Type ?u.1129080\nE₃ : Type ?u.1129083\nF : Type ?u.1129086\nG : Type ?u.1129089\nι : Type ?u.1129092\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : AddCommGro... | [
904,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_left_injective | [] | [
689,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_biUnion_congr | [
{
"state_after": "α : Type u_2\nβ : Type ?u.316219\nγ : Type ?u.316222\nδ : Type ?u.316225\nι : Type u_1\nR : Type ?u.316231\nR' : Type ?u.316234\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : Set α\ns : Set ι\nt : ι → Set α\nhc : Se... | [
1861,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_mul_of_le_mul_of_nonneg_right | [] | [
440,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Topology/Homotopy/Contractible.lean | ContinuousMap.HomotopyEquiv.contractibleSpace_iff | [] | [
97,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
11
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.algebraMap_eq_map_map_submonoid | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝¹² : CommRing R\nM : Submonoid R\nS : Type u_4\ninst✝¹¹ : CommRing S\ninst✝¹⁰ : Algebra R S\nP : Type ?u.3321764\ninst✝⁹ : CommRing P\nRₘ : Type u_1\nSₘ : Type u_2\ninst✝⁸ : CommRing Rₘ\ninst✝⁷ : CommRing Sₘ\ninst✝⁶ : Algebra R Rₘ\ninst✝⁵ : Is... | [
1359,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1353,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | Commute.smul_left_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : Group α\ninst✝³ : MulAction α β\ninst✝² : Mul β\ninst✝¹ : SMulCommClass α β β\ninst✝ : IsScalarTower α β β\na b : β\nr : α\n⊢ Commute (r • a) b ↔ Commute a b",
"tactic": "rw [Commute.symm_iff, Commute.smul_right_i... | [
143,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_sub | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ -(a - b) = b - a",
"tactic": "simp [Int.sub_eq_add_neg, Int.add_comm]"
}
] | [
364,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
363,
11
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.row_eq_prod | [
{
"state_after": "case a.mk\nμ : YoungDiagram\ni a b : ℕ\n⊢ (a, b) ∈ row μ i ↔ (a, b) ∈ {i} ×ˢ Finset.range (rowLen μ i)",
"state_before": "μ : YoungDiagram\ni : ℕ\n⊢ row μ i = {i} ×ˢ Finset.range (rowLen μ i)",
"tactic": "ext ⟨a, b⟩"
},
{
"state_after": "case a.mk\nμ : YoungDiagram\ni a b : ℕ\n... | [
322,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.has_succ_of_type_succ_lt | [
{
"state_after": "α✝ : Type ?u.100761\nβ : Type ?u.100764\nγ : Type ?u.100767\nr✝ : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nα : Type u_1\nr : α → α → Prop\nwo : IsWellOrder α r\nh : ∀ (a : Ordinal), a < type r → succ a < type r\nx : α\n⊢ r x (enum r (succ (typein r x)) (_ : succ (typein r x) < type ... | [
361,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.ext | [] | [
112,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Order/Category/NonemptyFinLinOrdCat.lean | nonemptyFinLinOrdCat_dual_comp_forget_to_linOrdCat | [] | [
255,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
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