file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/GroupPower/Lemmas.lean | SemiconjBy.cast_nat_mul_cast_nat_mul | [] | [
1046,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1044,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.unop | [] | [
104,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.eq_X_sub_C' | [] | [
217,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/Iterate.lean | Monotone.iterate_le_of_le | [] | [
110,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_nil_left_iff | [
{
"state_after": "case nil\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.14750\nδ : Type ?u.14753\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\n⊢ [] = []",
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82,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.tail | [] | [
58,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.inv_fun_map | [] | [
237,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.length_nil | [] | [
583,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_iff_surjective | [] | [
686,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_zpow | [] | [
223,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/SubsetProperties.lean | Filter.mem_cocompact' | [] | [
534,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pushforward_apply_comp | [] | [
501,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_add_tsub_cancel | [
{
"state_after": "case h.e'_2.h.e'_5\nα : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhab : b ≤ a\nhcb : c ≤ b\n⊢ a - b = a - c - (b - c)",
... | [
67,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_mul_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\n⊢ coeff (p * X) (n + 1) = coeff p n",
"tactic": "simpa only [pow_one] using coeff_mul_X_pow p 1 n"
}
] | [
265,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.add_neg | [] | [
113,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_bot | [] | [
1342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1341,
1
] |
Std/Data/Array/Lemmas.lean | Array.SatisfiesM_mapIdxM | [
{
"state_after": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nas : Array α\nf : Fin (size as) → α → m β\nmotive : Nat → Prop\nh0 : motive 0\np : Fin (size as) → β → Prop\nhs : ∀ (i : Fin (size as)), motive i.val → SatisfiesM (fun x => p i x ∧ motive (i.val + 1))... | [
191,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
171,
1
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Std/Data/Int/Lemmas.lean | Int.add_nonneg | [] | [
820,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
819,
11
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | LinearMap.withSeminorms_induced | [
{
"state_after": "𝕜 : Type u_4\n𝕜₂ : Type u_2\n𝕝 : Type ?u.715682\n𝕝₂ : Type ?u.715685\nE : Type u_5\nF : Type u_3\nG : Type ?u.715694\nι : Type u_1\nι' : Type ?u.715700\ninst✝⁸ : NormedField 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : NormedField 𝕜₂\ninst✝⁴ : AddCommGroup F\ninst✝³ : Modul... | [
743,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.map_mk | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.37780\nβ : Type ?u.37783\nn n' m✝ : ℕ\ns : Sym α n\na b : α\nf : α → β\nm : Multiset α\nhc : ↑Multiset.card m = n\n⊢ ↑Multiset.card (Multiset.map f m) = n",
"tactic": "simp [hc]"
}
] | [
397,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.lift_comp_ι | [
{
"state_after": "R : Type u_1\ninst✝² : CommSemiring R\nX : Type u_2\nA : Type u_3\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\ng : FreeAlgebra R X →ₐ[R] A\n⊢ ↑(lift R) (↑(lift R).symm g) = g",
"state_before": "R : Type u_1\ninst✝² : CommSemiring R\nX : Type u_2\nA : Type u_3\ninst✝¹ : Semiring A\ninst✝ : Al... | [
372,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.get?_tail | [] | [
751,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
src/lean/Init/Core.lean | Quotient.inductionOn | [] | [
1371,
23
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1367,
11
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.isIso_unop_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y : Cᵒᵖ\nf : X ⟶ Y\n⊢ IsIso f.unop ↔ IsIso f",
"tactic": "rw [← isIso_op_iff f.unop, Quiver.Hom.op_unop]"
}
] | [
155,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integral_eq_of_tendsto | [] | [
502,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublistsLen_succ_cons | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nn : ℕ\na : α\nl : List α\n⊢ sublistsLen (n + 1) l ++ map (id ∘ cons a) (sublistsLen n l) = sublistsLen (n + 1) l ++ map (cons a) (sublistsLen n l)",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nn : ℕ\na : α\nl : List... | [
276,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.neg_mem_iff | [] | [
563,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
11
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.opRingEquiv_symm_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nr : Rᵐᵒᵖ\n⊢ ↑(opRingEquiv R) (↑(RingEquiv.symm (opRingEquiv R)) (↑(monomial n) r)) =\n ↑(opRingEquiv R) (op (↑(monomial n) (unop r)))",
"tactic": "simp"
}
] | [
73,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_injective' | [] | [
313,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.prod_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type u_2\nR : Type u_5\nR₂ : Type ?u.588552\nK : Type ?u.588555\nM : Type u_3\nM' : Type u_4\nM'' : Type ?u.588564\nV : Type u\nV' : Type ?u.588569\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid M'\... | [
769,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.affineIndependent_of_toMatrix_right_inv | [
{
"state_after": "ι : Type u₁\nk : Type u₂\nV : Type u₃\nP : Type u₄\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : AffineSpace V P\ninst✝⁴ : Ring k\ninst✝³ : Module k V\nb : AffineBasis ι k P\nι' : Type u_1\ninst✝² : Fintype ι'\ninst✝¹ : Fintype ι\nb₂ : AffineBasis ι k P\ninst✝ : DecidableEq ι'\np : ι' → P\nA : Matrix ι ι... | [
79,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | nnnorm_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.217000\nγ : Type ?u.217003\nι : Type ?u.217006\ninst✝ : NormedDivisionRing α\na : α\n⊢ ↑‖a⁻¹‖₊ = ↑‖a‖₊⁻¹",
"tactic": "simp"
}
] | [
581,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_eq_support_max' | [] | [
683,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\na : α\nha : optParam (Set.Finite {a}) (_ : Set.Finite {a})\n⊢ ∀ (a_1 : α), a_1 ∈ Finite.toFinset ha ↔ a_1 ∈ {a}",
"tactic": "simp"
}
] | [
1055,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.seq_pure | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.294266\nι : Sort x\nf : Filter (α → β)\na : α\ns : Set (α → β)\nhs : s ∈ f\n⊢ (fun g => g a) '' s ∈ seq f (pure a)\n\ncase refine'_2\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.294266\nι : Sort x\nf : Filter (α → β)\na : α\ns... | [
2662,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2656,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_one_add_X_pow | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nS : Type v\na b : R✝\nn✝ m : ℕ\ninst✝¹ : Semiring R✝\np q r : R✝[X]\nR : Type u_1\ninst✝ : Semiring R\nn k : ℕ\n⊢ coeff ((1 + X) ^ n) k = ↑(Nat.choose n k)",
"tactic": "rw [add_comm _ X, coeff_X_add_one_pow]"
}
] | [
327,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/RingTheory/DedekindDomain/PID.lean | Ideal.eq_span_singleton_of_mem_of_not_mem_sq_of_not_mem_prime_ne | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\nP : Ideal R\nhP : IsPrime P\ninst✝¹ : IsDomain R\ninst✝ : IsDedekindDomain R\nx : R\nx_mem : x ∈ P\nhxP2 : ¬x ∈ P ^ 2\nhxQ : ∀ (Q : Ideal R), IsPrime Q → Q ≠ P → ¬x ∈ Q\nthis : DecidableEq (Ideal R) := Classical.decEq (Ideal R)\n⊢ P = span {x}",
"state_be... | [
80,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
src/lean/Init/Data/String/Basic.lean | String.set_next_add | [
{
"state_after": "s : String\ni : Pos\nc : Char\nb₁ b₂ : Nat\nh : i.byteIdx + csize (utf8GetAux s.data 0 i) + b₁ = utf8ByteSize.go s.data + b₂\n⊢ i.byteIdx + csize (utf8GetAux (utf8SetAux c s.data 0 i) 0 i) + b₁ = utf8ByteSize.go (utf8SetAux c s.data 0 i) + b₂",
"state_before": "s : String\ni : Pos\nc : Cha... | [
442,
24
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
424,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.id_comp | [] | [
329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhds_iff_exists_Ioo_subset | [] | [
1325,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.injective | [] | [
342,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
11
] |
Std/Data/List/Lemmas.lean | List.append_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl₁ l₂ l : List α\n⊢ l₁ ++ l₂ ⊆ l ↔ l₁ ⊆ l ∧ l₂ ⊆ l",
"tactic": "simp [subset_def, or_imp, forall_and]"
}
] | [
263,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
262,
9
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | Continuous.const_clm_comp | [] | [
949,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | LocalRing.closedPoint_mem_iff | [
{
"state_after": "case mp\nR : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : LocalRing R\nU : TopologicalSpace.Opens (PrimeSpectrum R)\n⊢ closedPoint R ∈ U → U = ⊤\n\ncase mpr\nR : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : LocalRing R\nU : TopologicalSpace.Ope... | [
1009,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero | [
{
"state_after": "no goals",
"state_before": "z : ℂ\nhre : z.re < 0\nhim : z.im = 0\n⊢ Tendsto log (𝓝[{z | 0 ≤ z.im}] z) (𝓝 (↑(Real.log (↑abs z)) + ↑π * I))",
"tactic": "simpa only [log, arg_eq_pi_iff.2 ⟨hre, him⟩] using\n (continuousWithinAt_log_of_re_neg_of_im_zero hre him).tendsto"
}
] | [
212,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_id_obj_unop | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma_mem | [
{
"state_after": "N✝ N : ℕ\nγ : SL(2, ℤ)\n⊢ ↑(SpecialLinearGroup.map (Int.castRingHom (ZMod N))) γ = 1 ↔\n ↑(↑γ 0 0) = 1 ∧ ↑(↑γ 0 1) = 0 ∧ ↑(↑γ 1 0) = 0 ∧ ↑(↑γ 1 1) = 1",
"state_before": "N✝ N : ℕ\nγ : SL(2, ℤ)\n⊢ γ ∈ Gamma N ↔ ↑(↑γ 0 0) = 1 ∧ ↑(↑γ 0 1) = 0 ∧ ↑(↑γ 1 0) = 0 ∧ ↑(↑γ 1 1) = 1",
"tactic":... | [
69,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Opposite.lean | Opposite.unop_inj_iff | [] | [
84,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_len_le_digits_len_succ | [
{
"state_after": "case inl\nn b : ℕ\n⊢ List.length (digits b 0) ≤ List.length (digits b (0 + 1))\n\ncase inr\nn✝ b n : ℕ\nhn : n ≠ 0\n⊢ List.length (digits b n) ≤ List.length (digits b (n + 1))",
"state_before": "n✝ b n : ℕ\n⊢ List.length (digits b n) ≤ List.length (digits b (n + 1))",
"tactic": "rcases... | [
438,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_cSup | [
{
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1350,
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Mathlib/Data/Num/Lemmas.lean | ZNum.of_nat_toZNum | [] | [
1547,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1546,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.symm_trans | [] | [
928,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
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Mathlib/Order/BoundedOrder.lean | min_eq_top | [] | [
883,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.infty_not_mem_range_coe | [] | [
160,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Data/Fin/Basic.lean | Fin.le_val_last | [
{
"state_after": "n m : ℕ\ni : Fin (n + 1)\n⊢ i ≤ last n",
"state_before": "n m : ℕ\ni : Fin (n + 1)\n⊢ i ≤ ↑n",
"tactic": "rw [Fin.cast_nat_eq_last]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\ni : Fin (n + 1)\n⊢ i ≤ last n",
"tactic": "exact Fin.le_last i"
}
] | [
825,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.interior | [
{
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594,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
11
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Mathlib/Data/Finset/Basic.lean | Finset.inter_insert_of_not_mem | [
{
"state_after": "no goals",
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... | [
1671,
92
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1670,
1
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Mathlib/Logic/Function/Conjugate.lean | Function.Commute.id_right | [] | [
123,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_sub | [] | [
336,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.exists_vecMul_eq_zero_iff | [
{
"state_after": "no goals",
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180,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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src/lean/Init/Core.lean | Quot.exists_rep | [] | [
1240,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1239,
1
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_of_one_le_inv | [
{
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"state_before": "α : Type u\ninst✝¹ : Lattice α\ninst✝ : CommGroup α\na : α\nh : 1 ≤ a⁻¹\n⊢ a⁻ = a⁻¹",
"tactic": "rw [neg_eq_pos_inv]"
},
{
"state_after": "no goals",
"state_before": "α ... | [
493,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.and_left_comm | [
{
"state_after": "no goals",
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"tactic": "decide"
}
] | [
170,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_inter_ne_empty_iff' | [
{
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976,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
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Mathlib/Order/ModularLattice.lean | IsModularLattice.sup_inf_sup_assoc | [] | [
232,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Std/Data/Array/Lemmas.lean | Array.SatisfiesM_foldrM | [
{
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153,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
139,
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Mathlib/Algebra/Squarefree.lean | multiplicity.finite_prime_left | [
{
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"tactic": "revert hb"
}... | [
141,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Logic/Equiv/Fintype.lean | Equiv.Perm.viaFintypeEmbedding_apply_mem_range | [
{
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"... | [
84,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Data/Nat/Bitwise.lean | Nat.zero_lor' | [
{
"state_after": "no goals",
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}
] | [
208,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_one | [] | [
93,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.iteratedFDeriv_comp_left | [
{
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253,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_comp | [] | [
987,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_span_mul_finite_of_mem_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type ?u.673289\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.673742\ninst✝¹ : Co... | [
867,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_of_Ici | [
{
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1072,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.nnnorm_ofSubsingleton | [] | [
524,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_lt_atBot | [] | [
222,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.inl_left_mul_inr_right | [
{
"state_after": "no goals",
"state_before": "N : Type u_1\nG : Type u_2\nH : Type ?u.94951\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\nx : N ⋊[φ] G\n⊢ ↑inl x.left * ↑inr x.right = x",
"tactic": "ext <;> simp"
}
] | [
174,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTrivAt_source | [] | [
710,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.find_lt_iff | [] | [
830,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.disjoint_withBotCoe | [
{
"state_after": "ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ ↑I ⊓ ↑J ≤ ⊥ ↔ ↑I ∩ ↑J ⊆ ↑⊥",
"state_before": "ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ Disjoint ↑I ↑J ↔ Disjoint I J",
"tactic": "simp only [disjoint_iff_inf_le, ← withBotCoe_subset_iff, coe_in... | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.coe_lt_degree | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ : Semiring S\np : R[X]\nn : ℕ\nh : p = 0\n⊢ ↑n < degree p ↔ n < natDegree p\n\ncase neg\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ :... | [
286,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.comp_mul_le | [] | [
392,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_equivMapOfInjective_apply | [] | [
3192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3190,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.not_mem_sInter_of_not_mem | [] | [
1088,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.equiv_pure_of_mem | [] | [
1039,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Deprecated/Group.lean | IsAddGroupHom.sub | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ✝ : Type v\nα : Type u_1\nβ : Type u_2\ninst✝¹ : AddGroup α\ninst✝ : AddCommGroup β\nf g : α → β\nhf : IsAddGroupHom f\nhg : IsAddGroupHom g\n⊢ IsAddGroupHom fun a => f a - g a",
"tactic": "simpa only [sub_eq_add_neg] using hf.add hg.neg"
}
] | [
410,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.nat_mul_eq | [] | [
274,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_filterMap | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nR S T : α → α → Prop\na : α\nl✝ : List α\nf : β → Option α\nl : List β\n_S : β → β → Prop := fun a a' => ∀ (b : α), b ∈ f a → ∀ (b' : α), b' ∈ f a' → R b b'\n⊢ Pairwise R (filterMap f l) ↔ Pairwise (fun a a' => ∀ (b : α), b ∈ f a → ∀ (b' : α), b' ∈ f a' → R b b') l"... | [
212,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.lt_succ_self | [] | [
104,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_iInf_of_map_univ | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.26409\nι : Sort u_3\nf✝ f₁ f₂ : Filter α\ng✝ g₁ g₂ : Set α → Filter β\nf : ι → Filter α\ng : Set α → Filter β\nhg : ∀ (s t : Set α), g (s ∩ t) = g s ⊓ g t\nhg' : g univ = ⊤\nh✝ : IsEmpty ι\n⊢ Filter.lift (iInf f) g = ⨅ (i : ι), Filter.lift (f i... | [
229,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Std/Data/Int/DivMod.lean | Int.div_nonneg | [] | [
94,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
92,
11
] |
Mathlib/Order/Lattice.lean | lt_sup_of_lt_left | [] | [
161,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | not_mem_of_csSup_lt | [] | [
603,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.sphere_zero_right | [
{
"state_after": "no goals",
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"tactic": "simp [sphere]"
}
] | [
98,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.unifIntegrable_of | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf✝ : ℕ → α → β\ng✝ : α → β\nhp : 1 ≤ p\nhp' : p ≠ ⊤\nf : ι → α → β\nhf : ∀ (i : ι), AEStronglyMeasurable (f i) μ\nh : ∀ (ε : ℝ), 0 < ε → ∃ C, ∀ (i : ι), snorm (Set.indicator ... | [
725,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.lintegral_div_right_eq_self | [
{
"state_after": "𝕜 : Type ?u.31885\nM : Type ?u.31888\nα : Type ?u.31891\nG : Type u_1\nE : Type ?u.31897\nF : Type ?u.31900\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\nμ : Measure G\nf✝ : G → E\ng✝ : G\ninst✝² ... | [
89,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.tendsto_set_lintegral_zero | [
{
"state_after": "α : Type u_2\nβ : Type ?u.795368\nγ : Type ?u.795371\nδ : Type ?u.795374\nm : MeasurableSpace α\nμ ν : Measure α\nι : Type u_1\nf : α → ℝ≥0∞\nh : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\nl : Filter ι\ns : ι → Set α\nhl : ∀ (i : ℝ≥0∞), 0 < i → ∀ᶠ (a : ι) in l, (↑↑μ ∘ s) a < i\n⊢ ∀ (i : ℝ≥0∞), 0 < i → ∀ᶠ (a : ... | [
522,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_pow | [
{
"state_after": "case succ\nm n✝ : ℤ\nn : ℕ\nih : Even (m ^ n) ↔ Even m ∧ n ≠ 0\n⊢ Even m → ¬n = 0 → Even m",
"state_before": "m n✝ : ℤ\nn : ℕ\n⊢ Even (m ^ n) ↔ Even m ∧ n ≠ 0",
"tactic": "induction' n with n ih <;> simp [*, even_mul, pow_succ]"
},
{
"state_after": "no goals",
"state_before... | [
160,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.algHom_ext | [] | [
186,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | LinearMap.coe_toAffineMap | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
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