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/Seq/WSeq.lean | Stream'.WSeq.exists_of_mem_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nf : α → WSeq β\nb : β\nh : b ∈ bind s f\nt : WSeq β\ntm : t ∈ map f s\nbt : b ∈ t\na : α\nas : a ∈ s\ne : f a = t\n⊢ b ∈ f a",
"tactic": "rwa [e]"
}
] | [
1477,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | isometry_iff_nndist_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.88\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nf : α → β\n⊢ Isometry f ↔ ∀ (x y : α), nndist (f x) (f y) = nndist x y",
"tactic": "simp only [Isometry, edist_nndist, ENNReal.coe_eq_coe]"
}
] | [
46,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.exists_lipschitz_retraction_of_isClosed | [
{
"state_after": "E : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\ns : Set ((n : ℕ) → E n)\nhs : IsClosed s\nhne : Set.Nonempty s\nf : ((n : ℕ) → E n) → (n : ℕ) → E n :=\n fun x => if x ∈ s then x else Set.Nonempty.some (_ : Set.Nonempty (s ∩ cylinder x (l... | [
697,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbit_nonempty | [] | [
76,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.right | [] | [
1100,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.top_mul_of_one_le | [
{
"state_after": "F : Type ?u.264796\nα : Type u_1\nβ : Type ?u.264802\nγ : Type ?u.264805\nδ : Type ?u.264808\nε : Type ?u.264811\ninst✝ : Monoid α\nf g : Filter α\ns✝ : Set α\na : α\nm n : ℕ\nhf : 1 ≤ f\ns : Set α\n⊢ s ∈ ⊤ * f → s ∈ ⊤",
"state_before": "F : Type ?u.264796\nα : Type u_1\nβ : Type ?u.264802... | [
704,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Analysis/Convex/Uniform.lean | exists_forall_closed_ball_dist_add_le_two_mul_sub | [
{
"state_after": "case inl\nE : Type u_1\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : UniformConvexSpace E\nε : ℝ\ninst✝ : NormedSpace ℝ E\nhε : 0 < ε\nr : ℝ\nhr : r ≤ 0\n⊢ ∃ δ, 0 < δ ∧ ∀ ⦃x : E⦄, ‖x‖ ≤ r → ∀ ⦃y : E⦄, ‖y‖ ≤ r → ε ≤ ‖x - y‖ → ‖x + y‖ ≤ 2 * r - δ\n\ncase inr\nE : Type u_1\ninst✝² : SeminormedAddC... | [
128,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_iInf | [] | [
351,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean | CategoryTheory.Limits.hasFiniteColimits_of_hasCoequalizers_and_finite_coproducts | [] | [
380,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.map_sentence | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\nN : Type u_4\nP : Type ?u.239981\nQ : Type ?u.239984\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\ninst✝ : Structure L Q\nf : M ↪ₑ[L] N\nφ : Sentence L\n⊢ M ⊨ φ ↔ N ⊨ φ",
"tactic": "rw [Sentence.Realize,... | [
114,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_add_right | [] | [
133,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsGroupHom.trivial_ker_of_injective | [
{
"state_after": "G : Type u_1\nH : Type u_2\nA : Type ?u.113567\na a₁ a₂ b c : G\ninst✝¹ : Group G\ninst✝ : Group H\nf : G → H\nhf : IsGroupHom f\nh : Injective f\nx : G\nhx : x ∈ ker f\n⊢ f x = f 1",
"state_before": "G : Type u_1\nH : Type u_2\nA : Type ?u.113567\na a₁ a₂ b c : G\ninst✝¹ : Group G\ninst✝ ... | [
467,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_pos | [] | [
176,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.drop_zero | [] | [
90,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
9
] |
Std/Data/Option/Lemmas.lean | Option.isSome_some | [] | [
53,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
53,
9
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_injective_of_injective | [] | [
961,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image_iInter₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.191070\nι : Sort u_3\nι' : Sort ?u.191076\nι₂ : Sort ?u.191079\nκ : ι → Sort u_4\nκ₁ : ι → Sort ?u.191089\nκ₂ : ι → Sort ?u.191094\nκ' : ι' → Sort ?u.191099\nf : α → β\nhf : Bijective f\ns : (i : ι) → κ i → Set α\n⊢ (f '' ... | [
1566,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1565,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodSumDistrib_symm_apply_left | [] | [
955,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.image_mulSingle_uIcc_left | [] | [
321,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_himp_right | [] | [
640,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/Finset/PImage.lean | Finset.pimage_empty | [
{
"state_after": "case a\nα : Type u_2\nβ : Type u_1\ninst✝² : DecidableEq β\nf g : α →. β\ninst✝¹ : (x : α) → Decidable (f x).Dom\ninst✝ : (x : α) → Decidable (g x).Dom\ns t : Finset α\nb a✝ : β\n⊢ a✝ ∈ pimage f ∅ ↔ a✝ ∈ ∅",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : DecidableEq β\nf g : α →. β\... | [
111,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.refl | [] | [
1101,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
1
] |
Mathlib/Data/List/Basic.lean | List.replicate_right_injective | [] | [
470,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Topology/UnitInterval.lean | projIcc_eq_zero | [] | [
185,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.comp_apply | [] | [
146,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Finmap.lean | Finmap.mem_lookup_union_middle | [] | [
610,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.of_cons | [] | [
53,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | AddSubgroup.coe_toIntSubmodule | [] | [
406,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Fintype/Sum.lean | Fintype.card_subtype_or_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15359\np q : α → Prop\nh : Disjoint p q\ninst✝² : Fintype { x // p x }\ninst✝¹ : Fintype { x // q x }\ninst✝ : Fintype { x // p x ∨ q x }\n⊢ card { x // p x ∨ q x } = card { x // p x } + card { x // q x }",
"tactic": "classical\n c... | [
134,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_differentiableOn_iff | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.174165\ninst✝... | [
196,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.exists_fin_two | [] | [
1772,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1771,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_const_smul_le | [] | [
1476,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ioc_of_Ioo | [] | [
663,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_neg | [
{
"state_after": "case h\nl : Type ?u.909484\nm : Type u_2\nn : Type u_1\no : Type ?u.909493\nm' : o → Type ?u.909498\nn' : o → Type ?u.909503\nR : Type ?u.909506\nS : Type ?u.909509\nα : Type v\nβ : Type w\nγ : Type ?u.909516\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : Fintype n\nv : n → α\nA : Matrix m n α\nx✝... | [
1913,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1911,
1
] |
Mathlib/Analysis/InnerProductSpace/Dual.lean | InnerProductSpace.innerSL_norm | [] | [
79,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.dvd_ord_compl_of_dvd_not_dvd | [
{
"state_after": "case inl\np d : ℕ\nhpd : ¬p ∣ d\nhdn : d ∣ 0\n⊢ d ∣ 0 / p ^ ↑(factorization 0) p\n\ncase inr\np d n : ℕ\nhdn : d ∣ n\nhpd : ¬p ∣ d\nhn0 : n ≠ 0\n⊢ d ∣ n / p ^ ↑(factorization n) p",
"state_before": "p d n : ℕ\nhdn : d ∣ n\nhpd : ¬p ∣ d\n⊢ d ∣ n / p ^ ↑(factorization n) p",
"tactic": "r... | [
568,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | AnalyticOn.deriv | [] | [
189,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_le_cons_iff | [] | [
572,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_rotate_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.209912\nP : Type u_3\nP' : Type ?u.209918\ninst✝⁷ : OrderedRing R\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module R V\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup V'\ninst✝² : Module R V'\ninst✝¹ : AddTorsor V' P'\ninst✝ : No... | [
386,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.eq_of_associated_right | [] | [
265,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/DirectLimit.lean | AddCommGroup.DirectLimit.of_f | [] | [
310,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_norm_zero' | [] | [
51,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.monic_X_pow | [] | [
827,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Order/Monotone/Basic.lean | Nat.rel_of_forall_rel_succ_of_lt | [] | [
982,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.neg | [] | [
414,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
8
] |
Mathlib/CategoryTheory/Limits/Final.lean | CategoryTheory.Functor.Final.colimit_cocone_comp_aux | [
{
"state_after": "case h₁\nC : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nF : C ⥤ D\ninst✝¹ : Final F\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\ns : Cocone (F ⋙ G)\nj : C\n⊢ ∀ (X₁ X₂ : C) (k₁ : F.obj j ⟶ F.obj X₁) (k₂ : F.obj j ⟶ F.obj X₂) (f : X₁ ⟶ X₂),\n k₁ ≫ F.map f = k₂ → G.map k₁ ... | [
260,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_singleton_eq_erase | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.245010\nγ : Type ?u.245013\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝¹ b a : α\ns : Finset α\na✝ : α\n⊢ a✝ ∈ s \\ {a} ↔ a✝ ∈ erase s a",
"state_before": "α : Type u_1\nβ : Type ?u.245010\nγ : Type ?u.245013\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\... | [
2222,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2220,
1
] |
Mathlib/Topology/Instances/Rat.lean | Nat.dist_cast_rat | [
{
"state_after": "x y : ℕ\n⊢ dist ↑↑x ↑↑y = dist ↑x ↑y",
"state_before": "x y : ℕ\n⊢ dist ↑x ↑y = dist x y",
"tactic": "rw [← Nat.dist_cast_real, ← Rat.dist_cast]"
},
{
"state_after": "no goals",
"state_before": "x y : ℕ\n⊢ dist ↑↑x ↑↑y = dist ↑x ↑y",
"tactic": "congr"
}
] | [
63,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Connected.lean | locallyConnectedSpace_of_connected_bases | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Type ?u.116895\nπ : ι✝ → Type ?u.116900\ninst✝ : TopologicalSpace α\ns t u v : Set α\nι : Type u_1\nb : α → ι → Set α\np : α → ι → Prop\nhbasis : ∀ (x : α), Filter.HasBasis (𝓝 x) (p x) (b x)\nhconnected : ∀ (x : α) (i : ι), p x i → IsPreconnected (b x i)\n⊢ ∀ (x :... | [
1211,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.inv_eq_self | [] | [
376,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.LHom.realize_onTerm | [
{
"state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.25879\nP : Type ?u.25882\ninst✝⁴ : Structure L M\ninst✝³ : Structure L N\ninst✝² : Structure L P\nα : Type u'\nβ : Type v'\ninst✝¹ : Structure L' M\nφ : L →ᴸ L'\ninst✝ : IsExpansionOn φ M\nv : α → M\n_a✝ : α\n⊢ Term.realize v (onTe... | [
216,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_linearDependent | [
{
"state_after": "case intro.intro.intro.intro.intro\nR : Type ?u.546412\ninst✝²⁰ : Semiring R\nM✝ : Type ?u.546418\ninst✝¹⁹ : AddCommMonoid M✝\ninst✝¹⁸ : Module R M✝\nN✝ : Type ?u.546450\ninst✝¹⁷ : AddCommMonoid N✝\ninst✝¹⁶ : Module R N✝\nP : Type ?u.546480\ninst✝¹⁵ : AddCommMonoid P\ninst✝¹⁴ : Module R P\nM' ... | [
819,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.hom_ext | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF : J ⥤ C\nt : Cocone F\nh : IsColimit t\nW : C\nf f' : t.pt ⟶ W\nw : ∀ (j : J), t.ι.app j ≫ f = t.ι.app j ≫ f'\n⊢ desc h { pt := W, ι := NatTrans.mk fun b => t.ι.app b ≫ f } =\n desc h { pt... | [
749,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Finset.prod_range | [] | [
41,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_clm_apply | [] | [
408,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.range_cons_cons_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.21814\nn' : Type ?u.21817\no' : Type ?u.21820\nx y : α\nu : Fin 0 → α\n⊢ Set.range (vecCons x (vecCons y u)) = {x, y}",
"tactic": "rw [range_cons, range_cons_empty, Set.singleton_union]"
}
] | [
186,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_add_zsmul | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ b + m • p - (toIocDiv hp a b • p + m • p) = b - toIocDiv hp a b • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : ... | [
419,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.mul_self_lt_mul_self | [] | [
290,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_mul | [
{
"state_after": "case ofFinsupp\nR : Type u\na b✝ : R\nm n : ℕ\ninst✝ : Semiring R\np q b : R[X]\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ ({ toFinsupp := toFinsupp✝ } * b).toFinsupp = { toFinsupp := toFinsupp✝ }.toFinsupp * b.toFinsupp",
"state_before": "R : Type u\na✝ b✝ : R\nm n : ℕ\ninst✝ : Semiring R\np q... | [
235,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_top' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.83091\nβ : Type ?u.83094\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a * ⊤ = if a = 0 then 0 else ⊤",
"tactic": "convert WithTop.mul_top' a"
}
] | [
549,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.not_sSameSide | [] | [
672,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.sub | [
{
"state_after": "m n a b c d : ℤ\nh₁ : a ≡ b [ZMOD n]\nh₂ : c ≡ d [ZMOD n]\n⊢ a + -c ≡ b + -d [ZMOD n]",
"state_before": "m n a b c d : ℤ\nh₁ : a ≡ b [ZMOD n]\nh₂ : c ≡ d [ZMOD n]\n⊢ a - c ≡ b - d [ZMOD n]",
"tactic": "rw [sub_eq_add_neg, sub_eq_add_neg]"
},
{
"state_after": "no goals",
"st... | [
187,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
11
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.zero_apply | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.norm_integral_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.541632\n𝕜 : Type ?u.541635\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nins... | [
741,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.succ_lt_succ_iff | [] | [
241,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearEquiv.prod_symm | [] | [
782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Filter.Tendsto.clog | [] | [
251,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_bit1 | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ fib (bit1 n) = fib (n + 1) ^ 2 + fib n ^ 2",
"tactic": "rw [Nat.bit1_eq_succ_bit0, bit0_eq_two_mul, fib_two_mul_add_one]"
}
] | [
191,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_sub | [
{
"state_after": "𝕜 : Type ?u.915894\nE : Type ?u.915897\nF : Type u_1\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace F\nv w : F\nh : ‖v‖ = ‖w‖\nR : F ≃ₗᵢ[ℝ] F := refle... | [
1007,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.regular_inv_iff | [
{
"state_after": "case mp\n𝕜 : Type ?u.524091\nG : Type u_1\nH : Type ?u.524097\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : MeasurableSpace H\ninst✝⁴ : TopologicalSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : T2Space G\n⊢ Regular (Measure.inv μ) → Regular μ\n\n... | [
519,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_le_neg_one_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.123535\nα : Type u_1\nβ : Type ?u.123541\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ ⌊a⌋ ≤ -1 ↔ a < 0",
"tactic": "rw [← zero_sub (1 : ℤ), floor_le_sub_one_iff, cast_zero]"
}
] | [
673,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.ker_isMaximal_of_surjective | [
{
"state_after": "R✝ : Type u\nS : Type v\nT : Type w\nR : Type u_1\nK : Type u_2\nF : Type u_3\ninst✝² : Ring R\ninst✝¹ : Field K\ninst✝ : RingHomClass F R K\nf : F\nhf : Function.Surjective ↑f\nJ : Ideal R\nx : R\nhJ : ker f ≤ J\nhxf : ¬x ∈ ker f\nhxJ : x ∈ J\n⊢ 1 ∈ J",
"state_before": "R✝ : Type u\nS : T... | [
2083,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2073,
1
] |
Mathlib/Topology/SubsetProperties.lean | Ultrafilter.le_nhds_lim | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nι : Type ?u.150954\nπ : ι → Type ?u.150959\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\ninst✝ : CompactSpace α\nF : Ultrafilter α\nx : α\nh : ↑F ≤ 𝓝 x\n⊢ ↑F ≤ 𝓝 (lim F)",
"state_before": "α : Type u\nβ : Type v\nι : Typ... | [
1220,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
8
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCoannihilator_dualAnnihilator_dualCoannihilator | [] | [
898,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.inner_indicatorConstLp_one | [
{
"state_after": "α : Type u_1\nE : Type ?u.160393\nF : Type ?u.160396\n𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\ns : Set α\nhs : MeasurableSet s\nhμs : ↑↑μ s ≠ ⊤\nf : { x // x ∈ Lp ... | [
279,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.lowerBounds_eq | [] | [
295,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.isMittagLeffler_iff_subset_range_comp | [
{
"state_after": "no goals",
"state_before": "J : Type u\ninst✝¹ : Category J\nF : J ⥤ Type v\ni j k : J\ns : Set (F.obj i)\ninst✝ : IsCofilteredOrEmpty J\n⊢ IsMittagLeffler F ↔ ∀ (j : J), ∃ i f, ∀ ⦃k : J⦄ (g : k ⟶ i), range (F.map f) ⊆ range (F.map (g ≫ f))",
"tactic": "simp_rw [isMittagLeffler_iff_eve... | [
232,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_biUnion_finset_eq | [] | [
2748,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2746,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_lineMap_left | [] | [
103,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_c_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.583385\nF : Type ?u.583388\nK : Type ?u.583391\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\n⊢ degree (toPoly P) ≤ 0",
"tactic": "simpa only [of_c_eq_zero ha hb hc] using degr... | [
350,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | MonoidHom.map_finprod_pLift | [
{
"state_after": "G : Type ?u.47261\nM : Type u_1\nN : Type u_2\nα : Sort u_3\nβ : Sort ?u.47273\nι : Sort ?u.47276\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : M →* N\ng : α → M\nh : Set.Finite (mulSupport (g ∘ PLift.down))\n⊢ mulSupport ((fun x => ↑f (g x)) ∘ PLift.down) ⊆ ↑(Finite.toFinset h)",
"sta... | [
302,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/PFun.lean | PFun.dom_of_mem_fix | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.19159\nδ : Type ?u.19162\nε : Type ?u.19165\nι : Type ?u.19168\nf : α →. β ⊕ α\na : α\nb : β\nh : b ∈ fix f a\nh₁ : Acc (fun x y => Sum.inr x ∈ f y) a\nh₂ :\n b ∈\n WellFounded.fixF\n (fun a IH =>\n Part.assert (f a).Dom fun hf =>\n ... | [
266,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.leibniz | [] | [
129,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_castSucc | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.8633\nβ : Type u_1\ninst✝ : CommMonoid β\nn : ℕ\nf : Fin (n + 1) → β\n⊢ ∏ i : Fin (n + 1), f i = (∏ i : Fin n, f (↑castSucc i)) * f (last n)",
"tactic": "simpa [mul_comm] using prod_univ_succAbove f (last n)"
}
] | [
95,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.mapRange_add | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.336628\nm inst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace β\nM : Type u_2\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : TopologicalSpace M\nv✝ : VectorMeasure α M\nN : Type u_3\ninst✝³ : AddCommMonoid N\ninst✝² : TopologicalSpace N\ninst✝¹ : ContinuousAdd M\ninst✝ ... | [
645,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsCompact.exists_thickening_subset_open | [] | [
1282,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.lex_inr_inr | [
{
"state_after": "case inr\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.28729\nδ : Type ?u.28732\nr r₁ r₂ : α → α → Prop\ns s₁ s₂ : β → β → Prop\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α ⊕ β\nh✝ : s b₁ b₂\n⊢ s b₁ b₂",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.... | [
488,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.norm_comp_le | [] | [
659,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | map_mul_map_eq_map_mul_map | [
{
"state_after": "F : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.29208\nδ : Type ?u.29211\nG : Type ?u.29214\ninst✝⁶ : FunLike F α fun x => β\ninst✝⁵ : CommMonoid α\ninst✝⁴ : CommMonoid β\ninst✝³ : CommMonoid γ\ninst✝² : CommMonoid δ\ninst✝¹ : CommGroup G\nA : Set α\nB : Set β\nC : Set γ\nn : ℕ\na b c d ... | [
153,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousAt.inner | [] | [
2274,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2272,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.range_eq_univ | [
{
"state_after": "R : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.1303609\nR₄ : Type ?u.1303612\nE : Type u_3\nE₂ : Type u_4\nE₃ : Type ?u.1303621\nE₄ : Type ?u.1303624\nF : Type ?u.1303627\n𝓕 : Type ?u.1303630\ninst✝³³ : Semiring R\ninst✝³² : Semiring R₂\ninst✝³¹ : Semiring R₃\ninst✝³⁰ : Semiring R₄\nσ₁₂ : R →+* R₂... | [
654,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_ofReal_re | [] | [
969,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.maxDegree_le_of_forall_degree_le | [
{
"state_after": "case pos\nι : Sort ?u.294725\n𝕜 : Type ?u.294728\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\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nk : ℕ\nh : ∀ (v : V), degree G v ≤ k\nhV : Finset.Nonempty univ\n⊢ maxDegree G ≤ k\n\ncase ... | [
1576,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | Subgroup.pow_index_mem | [
{
"state_after": "no goals",
"state_before": "G✝ : Type u\nA : Type v\nx y : G✝\na b : A\nn m : ℕ\ninst✝⁴ : Group G✝\ninst✝³ : AddGroup A\ninst✝² : Fintype G✝\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\ng : G\n⊢ g ^ index H ∈ H",
"tactic": "rw [← eq_one_iff, QuotientGroup.mk_pow H... | [
948,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_coe_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.29\nι : Type ?u.32\nα : Type u_1\nβ : Type ?u.38\ninst✝ : DivisionRing α\nn : ℤ\n⊢ ↑n / ↑1 = ↑n",
"tactic": "rw [Nat.cast_one, div_one]"
}
] | [
49,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.congr_app | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G H I : C ⥤ D\nα β : F ⟶ G\nh : α = β\nX : C\n⊢ α.app X = β.app X",
"tactic": "rw [h]"
}
] | [
71,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_mk_eq_product | [
{
"state_after": "case a\nα : Type u_1\nα' : Type ?u.62414\nβ : Type u_2\nβ' : Type ?u.62420\nγ : Type ?u.62423\nγ' : Type ?u.62426\nδ : Type ?u.62429\nδ' : Type ?u.62432\nε : Type ?u.62435\nε' : Type ?u.62438\nζ : Type ?u.62441\nζ' : Type ?u.62444\nν : Type ?u.62447\ninst✝⁹ : DecidableEq α'\ninst✝⁸ : Decidable... | [
336,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.dickson_two | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.23113\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nk : ℕ\na : R\n⊢ dickson k a 2 = X ^ 2 - ↑C a * (3 - ↑k)",
"tactic": "simp only [dickson, sq]"
}
] | [
81,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.div | [] | [
339,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_one | [
{
"state_after": "G : Type ?u.30331\nM : Type u_1\nN : Type ?u.30337\nα : Sort u_2\nβ : Sort ?u.30343\nι : Sort ?u.30346\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nthis : (mulSupport fun x => (fun x => 1) x.down) ⊆ ↑∅\n⊢ (∏ᶠ (x : α), 1) = 1",
"state_before": "G : Type ?u.30331\nM : Type u_1\nN : Type ?u.... | [
199,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.