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/Data/Set/Lattice.lean | Set.iInter₂_mono' | [] | [
419,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.differentiableAt_cosh | [] | [
671,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Data/List/Permutation.lean | List.permutations'Aux_eq_permutationsAux2 | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.7760\nt : α\n⊢ permutations'Aux t [] = (permutationsAux2 t [] [[] ++ [t]] [] id).snd\n\ncase cons\nα : Type u_1\nβ : Type ?u.7760\nt a : α\nts : List α\nih : permutations'Aux t ts = (permutationsAux2 t [] [ts ++ [t]] ts id).snd\n⊢ permutations'Aux t (a :: ts... | [
143,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.existsUnique | [] | [
811,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_pos_iff_nontrivial_of_finite | [
{
"state_after": "α : Type u_1\nβ : Type ?u.81734\ninst✝¹ : MetricSpace α\ns : Set α\ninst✝ : Finite ↑s\n⊢ Set.Nontrivial s → 0 < einfsep s",
"state_before": "α : Type u_1\nβ : Type ?u.81734\ninst✝¹ : MetricSpace α\ns : Set α\ninst✝ : Finite ↑s\n⊢ 0 < infsep s ↔ Set.Nontrivial s",
"tactic": "rw [infsep_... | [
550,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Data/Set/Image.lean | Set.subset_range_iff_exists_image_eq | [] | [
799,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Algebra/Homology/Homology.lean | HomologicalComplex.imageToKernel_as_boundariesToCycles | [] | [
119,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/Topology/Order/Basic.lean | nhds_bot_order | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : Preorder α\ninst✝¹ : OrderBot α\ninst✝ : OrderTopology α\n⊢ 𝓝 ⊥ = ⨅ (l : α) (_ : ⊥ < l), 𝓟 (Iio l)",
"tactic": "simp [nhds_eq_order (⊥ : α)]"
}
] | [
1135,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.toIterator | [
{
"state_after": "l m r : List Char\nx✝ : Substring\nh : ValidFor l m r x✝\n⊢ Iterator.ValidFor (List.reverse l) (m ++ r) { s := x✝.str, i := x✝.startPos }",
"state_before": "l m r : List Char\nx✝ : Substring\nh : ValidFor l m r x✝\n⊢ Iterator.ValidFor (List.reverse l) (m ++ r) (Substring.toIterator x✝)",
... | [
824,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
821,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_div_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.32640\nG : Type ?u.32643\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a⁻¹ / b⁻¹ = b / a",
"tactic": "simp"
}
] | [
520,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_congr | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf g : ℂ → E\nc : ℂ\nR : ℝ\nhR : 0 ≤ R\nh : EqOn f g (sphere c R)\nθ : ℝ\nx✝ : θ ∈ [[0, 2 * π]]\n⊢ deriv (circleMap c R) θ • (fun z => f z) (circleMap c R θ) =\n de... | [
368,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.interior_compact_eq_empty | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.2548\nδ : Type ?u.2551\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ni : α → β\ndi✝ : DenseInducing i\ninst✝ : T2Space β\ndi : DenseInducing i\nhd : Dense (range iᶜ)\ns : Set α\nhs : IsCompact s\nx : α\nhx : x ∈ interior s\n⊢ False",
"st... | [
95,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Order/LiminfLimsup.lean | Antitone.isBoundedUnder_ge_comp | [] | [
1202,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
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Mathlib/Data/Int/Order/Basic.lean | Int.coe_nat_eq_zero | [] | [
79,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.epi_of_epi_map | [] | [
77,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | Filter.HasBasis.uniformity_of_nhds_one_swapped | [
{
"state_after": "α : Type u_2\nβ : Type ?u.175746\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\nι : Sort u_1\np : ι → Prop\nU : ι → Set α\nh : HasBasis (𝓝 1) p U\n⊢ HasBasis (Filter.comap (fun x => x.fst / x.snd) (𝓝 1)) p fun i => {x | x.fst / x.snd ∈ U i}",
"state_before": "α : Typ... | [
361,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.47570\ninst✝ : PartialOrder α\na b c : α\nhab : a ≤ b\n⊢ Ico a b ∪ {b} = Icc a b",
"tactic": "simpa only [dual_Ioc, dual_Icc] using Ioc_union_left hab.dual"
}
] | [
872,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.cancel_right | [] | [
976,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.apply_comp_ofLe | [] | [
220,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_gt_of_forall_exists_ge | [] | [
75,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoin | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring A\ninst✝⁴ : Algebra R A\ns✝ t : Set A\ninst✝³ : CommSemiring B\ninst✝² : Algebra R B\ninst✝¹ : Algebra A B\ninst✝ : IsScalarTower R A B\nr : A\ns : Set B\nB' : Subalgebra R B\nhs : r • s ⊆ ↑B'\nx : B\nhr : ↑(alg... | [
362,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.preimage_closedBall | [] | [
1045,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Data/List/Basic.lean | List.splitOn_nil | [] | [
2902,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2901,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndep.indep | [
{
"state_after": "Ω : Type u_1\nι : Type u_2\nm : ι → MeasurableSpace Ω\ninst✝ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nh_indep : iIndep m\ni j : ι\nhij : i ≠ j\n⊢ IndepSets ((fun x => MeasurableSet) i) ((fun x => MeasurableSet) j)",
"state_before": "Ω : Type u_1\nι : Type u_2\nm : ι → MeasurableSp... | [
297,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.sInf_adj_of_nonempty | [
{
"state_after": "case intro\nι : Sort ?u.22992\n𝕜 : Type ?u.22995\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 (SimpleGraph V)\nG : SimpleGraph V\nhG : G ∈ s\n⊢ (∀ (G : SimpleGraph V), G ∈ s → Adj G a b) → a ≠ b",
"state_before": "ι : So... | [
332,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | prevD_nat | [
{
"state_after": "ι : Type ?u.115833\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC✝ D✝ E : HomologicalComplex V c\nf✝ g : C✝ ⟶ D✝\nh k : D✝ ⟶ E\ni✝ : ι\nC D : CochainComplex V ℕ\ni : ℕ\nf : (i j : ℕ) → X C i ⟶ X D j\n⊢ f i (ComplexShape.prev (ComplexShape.up ℕ) i) ≫ d D (Complex... | [
125,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_mul_mul_conjTranspose | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.39086\nm : Type u_1\nn : Type u_3\nA✝ : Matrix n n α\ninst✝⁴ : NonUnitalSemiring α\ninst✝³ : StarRing α\ninst✝² : NonUnitalSemiring β\ninst✝¹ : StarRing β\ninst✝ : Fintype m\nA : Matrix m m α\nB : Matrix n m α\nhA : IsHermitian A\n⊢ IsH... | [
218,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsCompact.smul | [] | [
153,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_map_equiv_iff | [] | [
308,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_add_of_disjoint | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.158991\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\ninst✝ : DecidableEq σ\nh : Disjoint (vars p) (vars q)\n⊢ vars p ∪ vars q ⊆ vars (p + q)",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ :... | [
339,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
src/lean/Init/Data/List/Basic.lean | List.filterTR_loop_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\np : α → Bool\nas bs : List α\n⊢ filterTR.loop p as bs = reverse bs ++ filter p as",
"tactic": "induction as generalizing bs with\n| nil => simp [filterTR.loop, filter]\n| cons a as ih =>\n simp [filterTR.loop, filter]\n ... | [
251,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
243,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.mem_span_map | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\nP : Type ?u.194470\ninst✝⁴ : CommRing P\ng : R →+* P\nT : Submonoid P\nhy : M ≤ Submonoid.comap g T\nQ : Type ?u.195302\ninst✝³ : CommRing Q\ninst✝² : Algebra P Q\ninst✝¹ : IsLocalizati... | [
179,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/List/Basic.lean | List.pmap_eq_nil | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.330793\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nH : ∀ (a : α), a ∈ l → p a\n⊢ pmap f l H = [] ↔ l = []",
"tactic": "rw [← length_eq_zero, length_pmap, length_eq_zero]"
}
] | [
3158,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3157,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_apply_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.77113\nα : Type u_1\nβ : Type ?u.77119\nf g : Perm α\np : α → Prop\nx y z : α\n⊢ SameCycle f x (↑f y) ↔ SameCycle f x y",
"tactic": "rw [sameCycle_comm, sameCycle_apply_left, sameCycle_comm]"
}
] | [
150,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/RingTheory/FreeRing.lean | FreeRing.hom_ext | [] | [
98,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Part.lean | Part.some_union_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.95055\nγ : Type ?u.95058\ninst✝ : Union α\na b : α\n⊢ some a ∪ some b = some (a ∪ b)",
"tactic": "simp [union_def]"
}
] | [
859,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.two_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nι : Type ?u.157\ninst✝¹ : Semiring R\ninst✝ : CharP R 2\n⊢ 2 = 0",
"tactic": "rw [← Nat.cast_two, CharP.cast_eq_zero]"
}
] | [
31,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_univ | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.174866\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.174961\... | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Algebra/Associated.lean | irreducible_or_factor | [
{
"state_after": "α✝ : Type ?u.79346\nβ : Type ?u.79349\nγ : Type ?u.79352\nδ : Type ?u.79355\nα : Type u_1\ninst✝ : Monoid α\nx : α\nh : ¬IsUnit x\nthis : (p : Prop) → Decidable p\n⊢ Irreducible x ∨ ∃ a b, ¬IsUnit a ∧ ¬IsUnit b ∧ a * b = x",
"state_before": "α✝ : Type ?u.79346\nβ : Type ?u.79349\nγ : Type ... | [
231,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Order/Basic.lean | rel_imp_eq_of_rel_imp_le | [] | [
567,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Iic_disjoint_Ioi | [] | [
38,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.supp_eq | [
{
"state_after": "case h\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\ni : Fin2 n\nx : F α\nx✝ : α i\n⊢ x✝ ∈ supp x i ↔\n x✝ ∈ {u | ∀ (a : (P F).A) (f : MvPFunctor.B (P F) a ⟹ α), abs { fst := a, snd := f } = x → u ∈ f i '' univ}",
"state_before": "n : ℕ\nF : TypeVec ... | [
184,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | tendsto_of_liminf_eq_limsup | [] | [
215,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Order/CompleteLattice.lean | inf_biInf | [] | [
1285,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
1
] |
Mathlib/RingTheory/Adjoin/FG.lean | Subalgebra.fg_top | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS : Subalgebra R A\nh : FG ⊤\n⊢ FG (map (val S) ⊤)",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semi... | [
171,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_mapAddMonoidHom | [] | [
1220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_image_preimage_sigma_mk_eq_self | [
{
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1285,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_eq | [] | [
960,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.two_dvd_centralBinom_succ | [
{
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"state_before": "n : ℕ\n⊢ 2 ∣ centralBinom (n + 1)",
"tactic": "use (n + 1 + n).choose n"
},
{
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"state_before": "n : ℕ\n⊢ centralBinom (n + 1) = 2 * choose (n + 1 + n) n",
"tactic": "rw... | [
123,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.FamilyOfElements.Compatible.pullback | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nf : Y ⟶ X\nx : FamilyOfElements P S.arrows\nh : SieveCompatible x\n⊢ SieveCompatible (FamilyOfElements.pullback f x)",
"state_before": "C : Type u₁\ninst✝ : Category ... | [
340,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
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Mathlib/Algebra/Order/Nonneg/Field.lean | Nonneg.mk_zpow | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.op_smul_inter_ne_empty_iff | [
{
"state_after": "F : Type ?u.145512\nα : Type u_1\nβ : Type ?u.145518\nγ : Type ?u.145521\ninst✝¹ : Group α\ninst✝ : MulAction α β\ns✝ t✝ A B : Set β\na : α\nx✝ : β\ns t : Set α\nx : αᵐᵒᵖ\n⊢ Set.Nonempty (x • s ∩ t) ↔ ∃ a b, (a ∈ s ∧ b ∈ t) ∧ a⁻¹ * b = unop x",
"state_before": "F : Type ?u.145512\nα : Type... | [
990,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.snorm_indicator_const | [
{
"state_after": "α : Type u_1\nE : Type ?u.641361\nF : Type ?u.641364\nG : Type u_2\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ns : Set α\nhs✝ : MeasurableSet s\nc✝ : E\nf : α → E\nhf : AEStronglyMeasur... | [
606,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.isHomogeneous_iff_forall_subset | [] | [
144,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max'_insert | [
{
"state_after": "F : Type ?u.359873\nα : Type u_1\nβ : Type ?u.359879\nγ : Type ?u.359882\nι : Type ?u.359885\nκ : Type ?u.359888\ninst✝ : LinearOrder α\ns✝ : Finset α\nH✝ : Finset.Nonempty s✝\nx a : α\ns : Finset α\nH : Finset.Nonempty s\n⊢ IsGreatest (insert a ↑s) (max a (max' s H))",
"state_before": "F ... | [
1477,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_div_left_of_right_invariant | [
{
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"state_before": "G : ... | [
464,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coneOfIsSplitMono_ι | [] | [
1203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.isUnit_iff_singleton_aux | [
{
"state_after": "no goals",
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1151,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_nsmul | [
{
"state_after": "ι : Type ?u.14945\nα : Type u_1\nβ : Type ?u.14951\nγ : Type ?u.14954\ninst✝ : CommMonoid α\ns t : Multiset α\na : α\nm✝ : Multiset ι\nf g : ι → α\nm : Multiset α\n⊢ prod 0 = 1",
"state_before": "ι : Type ?u.14945\nα : Type u_1\nβ : Type ?u.14951\nγ : Type ?u.14954\ninst✝ : CommMonoid α\ns... | [
127,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.append_succ_castAdd_aux | [
{
"state_after": "case mk\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nα : Type u_1\nm n : ℕ\na : Fin (Nat.succ m) → α\nb : Fin (Nat.succ n) → α\nh : a (Fin.last m) = b 0\ni : ℕ\nhi : i < m\n⊢ Matrix.vecAppend (_ : Nat.succ (m + n) = m + Nat.succ n) (a ∘ ↑Fin.castSucc) b\n (Fin.succ (↑(F... | [
477,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicofork.snd_app_right | [
{
"state_after": "C : Type u\ninst✝ : Category C\nI : MultispanIndex C\nK : Multicofork I\na : I.L\n⊢ (MultispanIndex.multispan I).map (WalkingMultispan.Hom.snd a) ≫\n K.ι.app (WalkingMultispan.right (MultispanIndex.sndFrom I a)) =\n MultispanIndex.snd I a ≫ π K (MultispanIndex.sndFrom I a)",
"state... | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_prod_le | [] | [
782,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Order/Lattice.lean | Subtype.coe_inf | [] | [
1381,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.of_le | [] | [
388,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | map_mul_left_nhds_one₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.52656\nβ : Type ?u.52659\nG₀ : Type u_1\ninst✝² : TopologicalSpace G₀\ninst✝¹ : GroupWithZero G₀\ninst✝ : ContinuousMul G₀\na : G₀\nha : a ≠ 0\n⊢ map (fun x => a * x) (𝓝 1) = 𝓝 a",
"tactic": "rw [map_mul_left_nhds₀ ha, mul_one]"
}
] | [
289,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/List/Basic.lean | List.cons_get_drop_succ | [
{
"state_after": "case nil\nι : Type ?u.200056\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nn✝ : Fin (length l)\nn : Fin (length [])\n⊢ get [] n :: drop (↑n + 1) [] = drop ↑n []\n\ncase cons\nι : Type ?u.200056\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nn✝ : Fin (le... | [
2125,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2117,
1
] |
Mathlib/FieldTheory/Normal.lean | AlgEquiv.restrictNormal_trans | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\nK : Type ?u.382075\ninst✝¹⁸ : Field F\ninst✝¹⁷ : Field K\ninst✝¹⁶ : Algebra F K\nK₁ : Type u_3\nK₂ : Type u_5\nK₃ : Type u_4\ninst✝¹⁵ : Field F\ninst✝¹⁴ : Field K₁\ninst✝¹³ : Field K₂\ninst✝¹² : Field K₃\ninst✝¹¹ : Algebra F K₁\ninst✝¹⁰ : Algebra F... | [
369,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_self_homothety | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.52305\nV : Type u_2\nP : Type u_1\nW : Type ?u.52314\nQ : Type ?u.52317\ninst✝⁸ : SeminormedAddCommGroup V\ninst✝⁷ : PseudoMetricSpace P\ninst✝⁶ : NormedAddTorsor V P\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : MetricSpace Q\ninst✝³ : NormedAddTorsor W ... | [
156,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_smul | [] | [
432,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Holor.lean | Holor.zero_mul | [] | [
221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
8
] |
Mathlib/Algebra/Module/PointwisePi.lean | smul_pi_subset | [
{
"state_after": "case intro.intro\nK : Type u_1\nι : Type u_3\nR : ι → Type u_2\ninst✝ : (i : ι) → SMul K (R i)\nr : K\ns : Set ι\nt : (i : ι) → Set (R i)\ny : (i : ι) → R i\nh : y ∈ pi s t\ni : ι\nhi : i ∈ s\n⊢ (fun x => r • x) y i ∈ (r • t) i",
"state_before": "K : Type u_1\nι : Type u_3\nR : ι → Type u_... | [
35,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Algebra/Homology/Single.lean | ChainComplex.to_single₀_ext | [
{
"state_after": "case a\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZeroObject V\nC : ChainComplex V ℕ\nX : V\nf g : C ⟶ (single₀ V).obj X\nh : Hom.f f 0 = Hom.f g 0\n⊢ ↑(↑(toSingle₀Equiv C X) f) = ↑(↑(toSingle₀Equiv C X) g)",
"state_before": "V : Type u\ninst✝² : Category V\n... | [
262,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Basis.det_reindex | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝¹⁰ : CommRing R\nM : Type u_4\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nM' : Type ?u.2694483\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nι : Type u_2\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Fintype ι\ne✝ : Basis ι R M\nA : Type ?u.2695503\... | [
619,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.uniformIntegrable_average | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.1281704\nι : Type ?u.1281707\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf✝ : ι → α → β\nhp : 1 ≤ p\nf : ℕ → α → ℝ\nhf₁ : ∀ (i : ℕ), AEStronglyMeasurable (f i) μ\nhf₂ : UnifIntegrable f p μ\nhf₃ : ∃ C, ∀ (i : ℕ), sn... | [
970,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Data/List/Perm.lean | List.not_perm_nil_cons | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\nx : α\nl : List α\nx✝ : [] ~ x :: l\np : [] ~ x :: l := x✝\n⊢ False",
"tactic": "injection p.symm.eq_nil"
}
] | [
178,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_map | [] | [
256,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.pow | [
{
"state_after": "no goals",
"state_before": "m✝ n a b c d m : ℕ\nh : a ≡ b [MOD n]\n⊢ a ^ m ≡ b ^ m [MOD n]",
"tactic": "induction m with\n| zero => rfl\n| succ d hd =>\n rw[pow_succ, pow_succ]\n exact hd.mul h"
},
{
"state_after": "no goals",
"state_before": "case zero\nm n a b c d : ℕ\n... | [
138,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_le_of_limit | [
{
"state_after": "case H.H\nα✝ : Type ?u.120549\nβ✝ : Type ?u.120552\nγ : Type ?u.120555\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nc : Ordinal\nα : Type u_1\nr : α → α → Prop\ninst✝¹ : IsWellOrder α r\nβ : Type u_1\ns : β → β → Prop\ninst✝ : IsWellOrder β s\nh : IsLimit (type s)\nH : ∀ (b' : ... | [
515,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.map_add_le | [] | [
120,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.coe_ssubset_coe | [] | [
203,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.mk_zero | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Holor.lean | Holor.mul_right_distrib | [] | [
216,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_ringHom_mk | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq_of_add_equiv_zero | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : f + g ≈ 0\nthis : LimZero (f + g - 0)\n⊢ norm f = norm g",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : f + g ≈ 0\n⊢ norm f = norm g",
"tactic": "have : LimZero (f + g - 0) := h"
},
{
"state_after":... | [
433,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.comapFunIsLocallyFraction | [
{
"state_after": "case mk\nR : Type u\ninst✝² : CommRing R\nS : Type u\ninst✝¹ : CommRing S\nP : Type u\ninst✝ : CommRing P\nf : R →+* S\nU : Opens ↑(PrimeSpectrum.Top R)\nV : Opens ↑(PrimeSpectrum.Top S)\nhUV : V.carrier ⊆ ↑(PrimeSpectrum.comap f) ⁻¹' U.carrier\ns : (x : { x // x ∈ U }) → Localizations R ↑x\nh... | [
1095,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Iio_insert | [
{
"state_after": "case a\nι : Type ?u.118371\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : DecidableEq α\nb a✝ : α\n⊢ a✝ ∈ insert b (Iio b) ↔ a✝ ∈ Iic b",
"state_before": "ι : Type ?u.118371\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ :... | [
721,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_fst_prod | [] | [
924,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_eq | [] | [
161,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Logic/Pairwise.lean | Pairwise.eq | [] | [
46,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
11
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.tendsto_leftLim | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : ConditionallyCompleteLinearOrder β\ninst✝³ : TopologicalSpace β\ninst✝² : OrderTopology β\nf : α → β\nhf : Monotone f\nx✝ y : α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\nx : α\nh' : 𝓝[Iio x] x = ⊥\n⊢ Tendsto f... | [
171,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_hasBasis_open | [] | [
1036,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.one_mk_mul_one_mk | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.1848\nB : Type ?u.1851\nG : Type ?u.1854\nH : Type ?u.1857\nM : Type u_1\nN : Type u_2\nP : Type ?u.1866\ninst✝¹ : Monoid M\ninst✝ : Mul N\nb₁ b₂ : N\n⊢ (1, b₁) * (1, b₂) = (1, b₁ * b₂)",
"tactic": "rw [mk_mul_mk, mul_one]"
}
] | [
81,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/List/Basic.lean | List.dropLast_take | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.197224\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn : ℕ\nl : List α\nh : n < length l\n⊢ dropLast (take n l) = take (pred n) l",
"tactic": "simp [dropLast_eq_take, min_eq_left_of_lt h, take_take, pred_le]"
}
] | [
2080,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2078,
1
] |
Mathlib/Data/Vector/Zip.lean | Vector.zipWith_toList | [] | [
32,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Std/Data/List/Lemmas.lean | List.infix_concat | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ : List α✝\na : α✝\nx✝ : l₁ <:+: l₂\nL₁ L₂ : List α✝\nh : L₁ ++ l₁ ++ L₂ = l₂\n⊢ L₁ ++ l₁ ++ concat L₂ a = concat l₂ a",
"tactic": "simp [← h, concat_eq_append, append_assoc]"
}
] | [
1589,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1588,
1
] |
Mathlib/Topology/PathConnected.lean | Path.map_id | [
{
"state_after": "case a.h\nX : Type u_1\nY : Type ?u.306480\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.306495\nγ✝ γ : Path x y\nx✝ : ↑I\n⊢ ↑(map γ (_ : Continuous id)) x✝ = ↑γ x✝",
"state_before": "X : Type u_1\nY : Type ?u.306480\ninst✝¹ : TopologicalSpace X\ninst✝ : ... | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | Dfinsupp.toFinsupp_neg | [] | [
201,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Finsupp/Indicator.lean | Finsupp.indicator_apply | [
{
"state_after": "ι : Type u_1\nα : Type u_2\ninst✝¹ : Zero α\ns : Finset ι\nf : (i : ι) → i ∈ s → α\ni : ι\ninst✝ : DecidableEq ι\n⊢ (if H : i ∈ s then f i H else 0) = if hi : i ∈ s then f i hi else 0",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝¹ : Zero α\ns : Finset ι\nf : (i : ι) → i ∈ s → α\ni :... | [
60,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.irreducible | [
{
"state_after": "A : Type u_1\nB : Type u_2\nB' : Type ?u.150283\ninst✝⁴ : CommRing A\ninst✝³ : Ring B\ninst✝² : Algebra A B\nx : B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\nhx : IsIntegral A x\nf g : A[X]\nhf : Monic f\nhg : Monic g\nhe : f * g = minpoly A x\n⊢ f = 1 ∨ g = 1",
"state_before": "A : Type u_... | [
252,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.renameEquiv_symm | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
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