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/LinearAlgebra/Dimension.lean | Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 | [] | [
1063,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasStrictFDerivAt.rpow_const | [] | [
464,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.isLittleO_congr_left | [] | [
175,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sup_inf_distrib_right | [] | [
999,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
11
] |
Mathlib/Topology/Order/LowerTopology.lean | LowerTopology.isTopologicalBasis | [
{
"state_after": "case h.e'_3\nα : Type u_1\nβ : Type ?u.6266\ninst✝² : Preorder α\ninst✝¹ : TopologicalSpace α\ninst✝ : LowerTopology α\ns : Set α\n⊢ lowerBasis α = (fun f => ⋂₀ f) '' {f | Set.Finite f ∧ f ⊆ {s | ∃ a, Ici aᶜ = s}}",
"state_before": "α : Type u_1\nβ : Type ?u.6266\ninst✝² : Preorder α\ninst... | [
223,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_eq_bot_iff | [
{
"state_after": "case refine'_1\nk : Type u_1\nV₁ : Type u_2\nP₁ : Type u_3\nV₂ : Type u_5\nP₂ : Type u_4\nV₃ : Type ?u.555099\nP₃ : Type ?u.555102\ninst✝⁹ : Ring k\ninst✝⁸ : AddCommGroup V₁\ninst✝⁷ : Module k V₁\ninst✝⁶ : AffineSpace V₁ P₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module k V₂\ninst✝³ : AffineSpace ... | [
1543,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1540,
1
] |
Mathlib/Data/List/Join.lean | List.eq_iff_join_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.15921\nL L' : List (List α)\n⊢ join L = join L' ∧ map length L = map length L' → L = L'",
"state_before": "α : Type u_1\nβ : Type ?u.15921\nL L' : List (List α)\n⊢ L = L' ↔ join L = join L' ∧ map length L = map length L'",
"tactic": "refine' ⟨fun H => by simp ... | [
200,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_eq_dif | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.92752\nβ₂ : Type ?u.92755\nγ : Type ?u.92758\nι : Sort ?u.92761\nι' : Sort ?u.92764\nκ : ι → Sort ?u.92769\nκ' : ι' → Sort ?u.92774\ninst✝¹ : CompleteLattice α\nf g s t : ι → α\na✝ b : α\np : Prop\ninst✝ : Decidable p\na : p → α\n⊢ (⨆ (... | [
1119,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.le_stable | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : Type w\na : α\nm n : ℕ\nh : m ≤ n\nf : Stream' (Option α)\nal : ∀ ⦃n : ℕ⦄ ⦃a : α⦄, f n = some a → f (n + 1) = some a\n⊢ ↑{ val := f, property := al } m = some a → ↑{ val := f, property := al } n = some a",
"state_before": "α : Type u\nβ : Type v\nγ : Ty... | [
335,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuousOn_toNNReal | [] | [
131,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_union | [] | [
107,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/List/MinMax.lean | List.le_maximum_of_mem' | [] | [
363,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.tendsto_iterate_efixedPoint | [] | [
135,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.ext | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF G : C ⥤ D\nh_obj : ∀ (X : C), F.obj X = G.obj X\nh_map :\n autoParam\n (∀ (X Y : C) (f : X ⟶ Y), F.map f = eqToHom (_ : F.obj X = G.obj X) ≫ G.map f ≫ eqToHom (_ : G.obj Y = F.obj Y))\n ... | [
188,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.disjoint_ker_aeval_of_coprime | [
{
"state_after": "R : Type u\nS : Type ?u.672918\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : M →ₗ[R] M\np q : R[X]\nhpq : IsCoprime p q\n⊢ LinearMap.ker (↑(aeval f) p) ⊓ LinearMap.ker (↑(aeval f) q) ≤ ⊥",
"state_before": "R : Type u\nS ... | [
1003,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_neg | [] | [
601,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
11
] |
Mathlib/Data/PFun.lean | PFun.fix_stop | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.29782\nδ : Type ?u.29785\nε : Type ?u.29788\nι : Type ?u.29791\nf : α →. β ⊕ α\nb : β\na : α\nhb : Sum.inl b ∈ f a\n⊢ Sum.inl b ∈ f a ∨ ∃ a', Sum.inr a' ∈ f a ∧ b ∈ fix f a'",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.29782\nδ : Type ?... | [
311,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Symmetric.lean | ModuleCat.MonoidalCategory.braiding_inv_apply | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | smul_iterate | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.55417\nN : Type ?u.55420\nG : Type u_1\nH : Type u_2\ninst✝¹ : Monoid G\na : G\nn : ℕ\ninst✝ : MulAction G H\nb : H\n⊢ ((fun x => a • x)^[Nat.zero]) b = a ^ Nat.zero • b",
"tactic": "rw [iterate_zero, id.def, pow_zero, one_smul]"
},
{
"st... | [
182,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_add_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.213806\nα : Type u_1\nβ : Type ?u.213812\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ ⌈a + 1⌉ = ⌈a⌉ + 1",
"tactic": "rw [←ceil_add_int a (1 : ℤ), cast_one]"
}
] | [
1155,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
] |
Mathlib/Topology/Basic.lean | subset_closure | [] | [
420,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopicWith.trans | [] | [
574,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Data/List/AList.lean | AList.insert_union | [
{
"state_after": "case a.a.a\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns₁ s₂ : AList β\nn✝ : ℕ\na✝ : Sigma β\n⊢ a✝ ∈ get? (insert a b (s₁ ∪ s₂)).entries n✝ ↔ a✝ ∈ get? (insert a b s₁ ∪ s₂).entries n✝",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β... | [
483,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.abs_coe_lt_top | [] | [
1066,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_erase_ne | [] | [
455,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.inv_apply | [] | [
125,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
9
] |
Mathlib/Topology/Instances/Rat.lean | Rat.embedding_coe_real | [] | [
52,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.orthogonalFamily_self | [] | [
222,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/Hom/Aut.lean | AddAut.mul_def | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.eventually_ne_atBot | [] | [
241,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
11
] |
Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.Subcanonical.isSheaf_of_representable | [] | [
252,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ZNum\n⊢ ↑(succ n) = ↑n + 1",
"tactic": "rw [← add_one, cast_add, cast_one]"
}
] | [
1341,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1340,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.mul_le_iff_le_inv | [
{
"state_after": "a b r : ℝ≥0\nhr : r ≠ 0\nthis : 0 < r\n⊢ r * a ≤ b ↔ a ≤ r⁻¹ * b",
"state_before": "a b r : ℝ≥0\nhr : r ≠ 0\n⊢ r * a ≤ b ↔ a ≤ r⁻¹ * b",
"tactic": "have : 0 < r := lt_of_le_of_ne (zero_le r) hr.symm"
},
{
"state_after": "no goals",
"state_before": "a b r : ℝ≥0\nhr : r ≠ 0\n... | [
801,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Order/Monotone/Basic.lean | Nat.exists_strictAnti' | [] | [
1018,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
1
] |
Mathlib/Topology/Order.lean | continuous_le_dom | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.37692\nf : α → β\nι : Sort ?u.37699\nt₁ t₂ : TopologicalSpace α\nt₃ : TopologicalSpace β\nh₁ : t₂ ≤ t₁\nh₂ : t₁ ≤ induced f t₃\n⊢ t₂ ≤ induced f t₃",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.37692\nf : α → β\nι : Sort ?u.37699\nt₁ t₂ : Topolo... | [
727,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsUnit.continuousAt_const_smul_iff | [] | [
424,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
8
] |
Mathlib/Analysis/Convex/Basic.lean | convex_iff_pointwise_add_subset | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1834\nβ : Type ?u.1837\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 F\ns : Set E\nx : E\nhA : Convex 𝕜 s\na b : 𝕜\nha : 0 ≤ ... | [
85,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Fintype/List.lean | Multiset.lists_coe | [] | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.le_def' | [] | [
631,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_one_iff_of_nonneg | [] | [
581,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Topology/Constructions.lean | map_nhds_subtype_coe_eq_nhds | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.159306\nδ : Type ?u.159309\nε : Type ?u.159312\nζ : Type ?u.159315\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\np : α → Prop\na : α\nha : p a\nh : ∀ᶠ (x : α) in 𝓝 a, p x\n⊢ (fun x => p x) ∈ 𝓝 ↑{ val := a, property ... | [
1072,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1613274\nι : Type ?u.1613277\nE : Type u_2\nF : Type ?u.1613283\n𝕜 : Type ?u.1613286\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\ninst✝³ : NormedRing 𝕜\ninst✝² : M... | [
688,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.mem_uIcc_of_le | [] | [
925,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_neg_shift' | [] | [
492,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/List/Perm.lean | List.count_permutations'Aux_self | [
{
"state_after": "case nil\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nx✝ x : α\n⊢ count [x] (permutations'Aux x []) = length (takeWhile (fun b => decide ((fun x x_1 => x = x_1) x b)) []) + 1\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nx✝ y : α\nl : List ... | [
1375,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | infsInfHom_apply | [] | [
999,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/Topology/Order/Basic.lean | continuousWithinAt_Ioo_iff_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderClosedTopology α\na✝ b✝ : α\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace β\na b : α\nf : α → β\nh : a < b\n⊢ ContinuousWithinAt f (Ioo a b) a ↔ Conti... | [
451,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Init/CcLemmas.lean | eq_false_of_or_eq_false_left | [] | [
105,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.pi_bot | [
{
"state_after": "G : Type ?u.321013\nG' : Type ?u.321016\ninst✝⁵ : Group G\ninst✝⁴ : Group G'\nA : Type ?u.321025\ninst✝³ : AddGroup A\nH K : Subgroup G\nk : Set G\nN : Type ?u.321046\ninst✝² : Group N\nP : Type ?u.321052\ninst✝¹ : Group P\nη : Type u_1\nf : η → Type u_2\ninst✝ : (i : η) → Group (f i)\np : (i ... | [
1857,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1853,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | neg_iff_pos_of_mul_neg | [] | [
1204,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_singleton | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl : List α✝\na : α✝\n⊢ Disjoint l [a] ↔ ¬a ∈ l",
"tactic": "rw [disjoint_comm, singleton_disjoint]"
}
] | [
1381,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1380,
14
] |
Mathlib/Topology/Constructions.lean | Continuous.quotient_lift | [] | [
1167,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | omegaLimit_eq_iInter_inter | [
{
"state_after": "τ : Type u_1\nα : Type u_3\nβ : Type u_2\nι : Type ?u.36686\ninst✝ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\nv : Set τ\nhv : v ∈ f\n⊢ (⋂ (u : Set τ) (_ : u ∈ f), closure (image2 ϕ (u ∩ v) s)) = ⋂ (u : ↑f.sets), closure (image2 ϕ (↑u ∩ v) s)",
"state_before": "τ : ... | [
217,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.inv_mem_Icc_iff | [] | [
33,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Int/GCD.lean | Int.exists_gcd_one' | [] | [
382,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.NoetherianSpace.finite | [] | [
170,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | ContinuousOn.isSeparable_image | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.308958\nι : Type ?u.308961\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ\ns✝ : Set α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nhf : ContinuousOn f s\nhs : IsSeparable s\n⊢ IsSeparable ((fun x => f ↑x) '' univ)",
"state_before": "α : Type... | [
1956,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1953,
1
] |
Mathlib/Logic/Embedding/Basic.lean | subtypeOrLeftEmbedding_apply_left | [] | [
485,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.tendsto_approx | [] | [
1018,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
11
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_caratheodory | [
{
"state_after": "α : Type u_1\nβ : Type ?u.22040\nγ : Type ?u.22043\np : Pmf α\ns t : Set α\nx : MeasurableSpace α\nhx : x ∈ Set.range fun i => OuterMeasure.caratheodory (↑p i • dirac i)\n⊢ ⊤ ≤ x",
"state_before": "α : Type u_1\nβ : Type ?u.22040\nγ : Type ?u.22043\np : Pmf α\ns t : Set α\n⊢ OuterMeasure.c... | [
169,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.card_toEnumFinset | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nm✝ m : Multiset α\n⊢ ↑card (map Prod.fst (toEnumFinset m).val) = ↑card m",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nm✝ m : Multiset α\n⊢ Finset.card (toEnumFinset m) = ↑card m",
"tactic": "rw [Finset.card, ←Multiset.card_map Prod.fst m.... | [
253,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.subset_iff_eq_of_card_le | [] | [
275,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
src/lean/Init/Core.lean | beq_iff_eq | [
{
"state_after": "a✝ b✝ c d : Prop\nα : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\nh : a = b\n⊢ (a == b) = true",
"state_before": "a✝ b✝ c d : Prop\nα : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\n⊢ a = b → (a == b) = true",
"tactic": "intro h"
},
{
"state_after": "a✝ b ... | [
1170,
56
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1169,
9
] |
Mathlib/Order/Directed.lean | isDirected_mono | [] | [
209,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.le_comap_map | [] | [
2202,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2201,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_pair_add_mul_left | [
{
"state_after": "case h\nα : Type u\nβ : Type v\ninst✝¹ : Semiring α\nI : Ideal α\na b : α\nR : Type u\ninst✝ : CommRing R\nx y z x✝ : R\n⊢ x✝ ∈ span {x + y * z, y} ↔ x✝ ∈ span {x, y}",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Semiring α\nI : Ideal α\na b : α\nR : Type u\ninst✝ : CommRing R\nx y z... | [
382,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Algebra/Star/Basic.lean | RingHom.star_apply | [] | [
422,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_dvd_index_of_le | [] | [
114,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_nonneg_of_base_lt_one | [
{
"state_after": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhx' : x ≤ 1\n⊢ x ≤ 1",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhx' : x ≤ 1\n⊢ 0 ≤ logb b x",
"tactic": "rw [logb_nonneg_iff_of_base_lt_one b_pos b_lt_one hx]"
},
{
"state_after": "no goals"... | [
311,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder | [
{
"state_after": "case intro.intro\n𝕜 : Type ?u.303808\nE : Type ?u.303811\nF : Type ?u.303814\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf g g' : ℝ → ℝ\nx x₀ : ℝ\nn : ℕ\nhx : x₀ < x\nhf : ContDiffOn ℝ (↑n) f (Icc x₀ x)\nhf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc x₀ x)) (Ioo x₀ x)\ngc... | [
262,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | max_div_div_right_of_nonpos | [] | [
997,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.add_mem | [] | [
145,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.sum_int_mod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.171528\nα : Type ?u.171531\nβ : Type ?u.171534\nγ : Type ?u.171537\ns : Multiset ℤ\nn : ℤ\n⊢ sum s % n = sum (map (fun x => x % n) s) % n",
"tactic": "induction s using Multiset.induction <;> simp [Int.add_emod, *]"
}
] | [
536,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.inverseAssociator_map_inl | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearMap.toSpanSingleton_smul' | [
{
"state_after": "case h\n𝕜 : Type u_3\n𝕜₂ : Type ?u.392830\nE : Type u_2\nF : Type ?u.392836\nG : Type ?u.392839\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : NormedField 𝕜₂\ninst✝⁴ : SeminormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\n𝕜' : Type u_1\ninst✝² : NormedField 𝕜'\ninst✝¹ : NormedSpace 𝕜' E\ninst✝ : SMul... | [
258,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.lt_one_iff | [] | [
173,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | Dvd.dvd.linear_comb | [] | [
47,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ioo_of_le | [] | [
746,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.to_nil | [] | [
952,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_iff_ker_eq_bot | [] | [
77,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.equivOfEq_symm | [] | [
1090,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Agrees.get_eq' | [] | [
88,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/RingTheory/Coprime/Ideal.lean | Ideal.iSup_iInf_eq_top_iff_pairwise | [
{
"state_after": "ι : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nt : Finset ι\nh : Finset.Nonempty t\nI : ι → Ideal R\nthis : DecidableEq ι\n⊢ (⨆ (i : ι) (_ : i ∈ t), ⨅ (j : ι) (_ : j ∈ t) (_ : j ≠ i), I j) = ⊤ ↔ Set.Pairwise ↑t fun i j => I i ⊔ I j = ⊤",
"state_before": "ι : Type u_1\nR : Type u_2\nin... | [
115,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.eq_of_eq_on_source_univ | [
{
"state_after": "case refine_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.59180\nδ : Type ?u.59183\ne✝ : LocalEquiv α β\ne'✝ : LocalEquiv β γ\ne e' : LocalEquiv α β\nh : e ≈ e'\ns : e.source = univ\nt : e.target = univ\nx : α\n⊢ ↑e x = ↑e' x\n\ncase refine_2\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.59180\nδ : Ty... | [
913,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.degree_scaleRoots | [
{
"state_after": "A : Type ?u.34124\nK : Type ?u.34127\nR : Type u_1\nS : Type ?u.34133\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : R[X]\ns : R\nthis : (a : Prop) → Decidable a\n⊢ degree (scaleRoots p s) = degree p",
"state_befor... | [
85,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.mul_bind | [] | [
613,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableAt.prod_map | [] | [
353,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
11
] |
Mathlib/Topology/Algebra/Nonarchimedean/Bases.lean | RingSubgroupsBasis.hasBasis_nhds_zero | [
{
"state_after": "A : Type u_1\nι : Type u_2\ninst✝¹ : Ring A\ninst✝ : Nonempty ι\nB : ι → AddSubgroup A\nhB : RingSubgroupsBasis B\ns : Set A\n⊢ s ∈ 𝓝 0 ↔ ∃ i, True ∧ ↑(B i) ⊆ s",
"state_before": "A : Type u_1\nι : Type u_2\ninst✝¹ : Ring A\ninst✝ : Nonempty ι\nB : ι → AddSubgroup A\nhB : RingSubgroupsBas... | [
157,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.Represents.mul | [
{
"state_after": "ι : Type u_1\ninst✝⁴ : Fintype ι\nM : Type u_3\ninst✝³ : AddCommGroup M\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nb : ι → M\nhb : Submodule.span R (Set.range b) = ⊤\ninst✝ : DecidableEq ι\nA A' : Matrix ι ι R\nf f' : Module.End R M\nh : Represents b A f\nh' : Repres... | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.quot_mk_eq_coe | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wp_ind | [] | [
177,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.divOf_apply | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.hasTerminal_of_hasInitial_op | [] | [
437,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Bijective.existsUnique_iff | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort u_2\nγ : Sort ?u.7730\nf✝ f : α → β\nhf : Bijective f\np : β → Prop\nx✝ : ∃! y, p y\ny : β\nhpy : (fun y => p y) y\nhy : ∀ (y_1 : β), (fun y => p y) y_1 → y_1 = y\nx : α\nhx : f x = y\n⊢ (fun x => p (f x)) x",
"tactic": "simpa [hx]"
... | [
262,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_eq_of_forall_le_of_forall_lt_exists_gt | [] | [
875,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\n⊢ ↑n ≤ trailingDegree (X ^ n)",
"tactic": "simpa only [C_1, one_mul] using le_trailingDegree_C_mul_X_pow n (1 : R)"
}
] | [
287,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_X_add_C_of_natDegree_le_one | [] | [
460,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpTo.continuous | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1261,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_refl_left | [] | [
1212,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.eq_of_le | [] | [
87,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
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