file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_sdiff_eq_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.855554\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommGroup β\ninst✝ : DecidableEq α\nh : s₁ ⊆ s₂\n⊢ ∏ x in s₂ \\ s₁, f x = (∏ x in s₂, f x) / ∏ x in s₁, f x",
"tactic": "rw [eq_div_iff_mul_eq', prod_sdi... | [
1832,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1830,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_bit0 | [] | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.prod | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf✝ : α → β\nx✝ y✝ : α\nr : ℝ≥0∞\nf : α → β\nKf : ℝ≥0\nhf : LipschitzWith Kf f\ng : α → γ\nKg : ℝ≥0\nhg : LipschitzWith Kg g\nx y : α\n⊢ edist ((f... | [
251,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
11
] |
Mathlib/Algebra/Ring/Commute.lean | Commute.add_left | [] | [
44,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Analysis/SpecialFunctions/NonIntegrable.lean | not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured | [] | [
137,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsGLB.ciInf_set_eq | [] | [
564,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_nonempty | [] | [
641,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.subset_sups | [] | [
181,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_compSL_le | [] | [
936,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisors_subset_of_dvd | [] | [
146,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.unit_app_inverse | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\ne : C ≌ D\nY : D\n⊢ 𝟙 (e.inverse.obj Y) = 𝟙 (e.inverse.obj ((𝟭 D).obj Y))",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\ne : C ≌ D\nY : D\n⊢ (unit e).app (e.inverse.obj Y) = e.inver... | [
218,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.OpenNhdsOf.isOpen | [] | [
447,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
11
] |
Mathlib/NumberTheory/Divisors.lean | Nat.sum_properDivisors_eq_one_iff_prime | [
{
"state_after": "case zero\n\n⊢ ∑ x in properDivisors zero, x = 1 ↔ Prime zero\n\ncase succ\nn : ℕ\n⊢ ∑ x in properDivisors (succ n), x = 1 ↔ Prime (succ n)",
"state_before": "n : ℕ\n⊢ ∑ x in properDivisors n, x = 1 ↔ Prime n",
"tactic": "cases' n with n"
},
{
"state_after": "no goals",
"st... | [
422,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.Icc_eq | [] | [
178,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.nnnorm | [] | [
2060,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2058,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset_val | [] | [
3238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3237,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.rightInvOn | [] | [
279,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
11
] |
Mathlib/Combinatorics/Catalan.lean | Tree.treesOfNumNodesEq_zero | [
{
"state_after": "no goals",
"state_before": "⊢ treesOfNumNodesEq 0 = {nil}",
"tactic": "rw [treesOfNumNodesEq]"
}
] | [
182,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_coe_eq_bot_iff | [] | [
607,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.trans_tendsto | [] | [
1434,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1432,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.prod | [] | [
603,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.and_coe_iff | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ (a && b) = true ↔ a = true ∧ b = true",
"tactic": "simp"
}
] | [
165,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.map_closureS | [] | [
1225,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.balance'_aux | [
{
"state_after": "α : Type u_1\ninst✝ : Preorder α\nl : Ordnode α\nx : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nhl : Valid' o₁ l ↑x\nhr : Valid' (↑x) r o₂\nH₁ : 2 * size r ≤ 9 * size l + 5 ∨ size r ≤ 3\nH₂ : 2 * size l ≤ 9 * size r + 5 ∨ size l ≤ 3\n⊢ Valid' o₁\n (if size l + size r ≤ 1 then Ordnode... | [
1313,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1306,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.lt_toNat | [] | [
507,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Topology/Connected.lean | DenseRange.preconnectedSpace | [] | [
769,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousOn.cpow_const | [] | [
168,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.limitConstTerminal_inv_π | [
{
"state_after": "case w\nC✝ : Type u₁\ninst✝³ : Category C✝\nJ : Type u_1\ninst✝² : Category J\nC : Type u_3\ninst✝¹ : Category C\ninst✝ : HasTerminal C\nj : J\n⊢ ∀ (j_1 : Discrete PEmpty),\n (limitConstTerminal.inv ≫ limit.π ((Functor.const J).obj (⊤_ C)) j) ≫ limit.π (Functor.empty C) j_1 =\n termina... | [
468,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.zero_imI | [] | [
852,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
9
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.unmop_comp | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.isClique_bot_iff | [] | [
88,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.hasZeroObject_of_hasTerminal_object | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasTerminal C\nX : C\nf : ⊤_ C ⟶ X\n⊢ f = default",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasTerminal C... | [
562,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Data/Opposite.lean | Opposite.op_eq_iff_eq_unop | [] | [
106,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_mul_left_Icc' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a : α\nh : 0 < a\nb c : α\n⊢ (fun x x_1 => x * x_1) a '' Icc b c = Icc (a * b) (a * c)",
"tactic": "convert image_mul_right_Icc' b c h using 1 <;> simp only [mul_comm _ a]"
}
] | [
744,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_sub_center_inv | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.610728\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nc : ℂ\nR : ℝ\nhR : R ≠ 0\n⊢ (∮ (z : ℂ) in C(c, R), (z - c)⁻¹) = 2 * ↑π * I",
"tactic": "simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circl... | [
467,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_eval | [] | [
880,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_iff_tsub_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhb : AddLECancellable b\nhc : AddLECancellab... | [
134,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/Data/Quot.lean | Trunc.exists_rep | [] | [
504,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Algebra/Ring/Defs.lean | neg_eq_neg_one_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝¹ : MulOneClass α\ninst✝ : HasDistribNeg α\na : α\n⊢ -a = -1 * a",
"tactic": "simp"
}
] | [
321,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_strictMono | [] | [
83,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | associatedPrimes.eq_empty_of_subsingleton | [
{
"state_after": "case h\nR : Type u_2\ninst✝⁵ : CommRing R\nI J : Ideal R\nM : Type u_1\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nM' : Type ?u.60520\ninst✝² : AddCommGroup M'\ninst✝¹ : Module R M'\nf : M →ₗ[R] M'\ninst✝ : Subsingleton M\nx✝ : Ideal R\n⊢ x✝ ∈ associatedPrimes R M ↔ x✝ ∈ ∅",
"state_befo... | [
124,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.funCongrLeft_id | [] | [
2663,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2662,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.swap_fst | [] | [
62,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Connected.lean | mem_connectedComponentIn | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.46668\nπ : ι → Type ?u.46673\ninst✝ : TopologicalSpace α\ns t u v : Set α\nx : α\nF : Set α\nhx : x ∈ F\n⊢ x ∈ connectedComponentIn F x",
"tactic": "simp [connectedComponentIn_eq_image hx, mem_connectedComponent, hx]"
}
... | [
601,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_of_eq_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.119773\nι : Sort x\nf✝ g : Filter α\ns✝ t : Set α\nf : Filter α\ns : Set α\nh : f ⊓ 𝓟 (sᶜ) = ⊥\n⊢ s ∈ f",
"tactic": "rwa [inf_principal_eq_bot, compl_compl] at h"
}
] | [
1019,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_neg | [] | [
471,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
470,
25
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.uniformEmbedding | [] | [
183,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.exists_cos_eq_zero | [
{
"state_after": "no goals",
"state_before": "⊢ 1 ≤ 2",
"tactic": "norm_num"
}
] | [
125,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_dite_empty_left | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t✝ t₁ t₂ u : Set α\np : Prop\ninst✝ : Decidable p\nt : ¬p → Set α\nx : α\n⊢ (¬p ∧ ∀ (h : ¬p), x ∈ t h) ↔ ∃ h, x ∈ t h",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t✝ t₁ t₂ u : Set α\np :... | [
2227,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2224,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.IsNormal.apply_le_nfp | [
{
"state_after": "no goals",
"state_before": "f✝ : Ordinal → Ordinal\nf : Ordinal → Ordinal\nH : IsNormal f\na b : Ordinal\nh : b ≤ nfp f a\n⊢ f b ≤ nfp f a",
"tactic": "simpa only [H.nfp_fp] using H.le_iff.2 h"
}
] | [
491,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.comap_uniformity_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.10552\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nhf : AntilipschitzWith K f\nε : ℝ≥0∞\nh₀ : 0 < ε\n⊢ ∃ i, 0 < i ∧ Prod.map f f ⁻¹' {p | edist p.fst p.snd < i} ⊆ {p | edist p.fst p.snd ... | [
172,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ker_codRestrict | [] | [
1022,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Set.EquicontinuousAt.continuousAt_of_mem | [] | [
162,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | le_hasSum_of_le_sum | [] | [
60,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_le_max | [
{
"state_after": "case inl\na b : Cardinal\nha : ℵ₀ ≤ a\n⊢ a + b ≤ max (max a b) ℵ₀\n\ncase inr\na b : Cardinal\nha : a < ℵ₀\n⊢ a + b ≤ max (max a b) ℵ₀",
"state_before": "a b : Cardinal\n⊢ a + b ≤ max (max a b) ℵ₀",
"tactic": "cases' le_or_lt ℵ₀ a with ha ha"
},
{
"state_after": "case inl\na b ... | [
756,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Algebra/Bounds.lean | mul_mem_upperBounds_mul | [] | [
104,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_smul_vsub_vadd_right | [] | [
361,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_limit | [
{
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"tactic": "apply le_antisymm _ (ci... | [
286,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
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Mathlib/Algebra/GroupPower/Order.lean | one_le_pow_iff_of_nonneg | [
{
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573,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_blsub_of_lt_succ_limit | [
{
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1874,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1870,
1
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Mathlib/Algebra/Ring/Prod.lean | NonUnitalRingHom.prod_comp_prodMap | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/Complex/Schwarz.lean | Complex.norm_deriv_le_div_of_mapsTo_ball | [
{
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"tactic": "simpa only [dslo... | [
148,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closedBall_subset_cthickening_singleton | [
{
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1093,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
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Mathlib/CategoryTheory/Preadditive/Projective.lean | CategoryTheory.Projective.projective_iff_preservesEpimorphisms_coyoneda_obj | [] | [
147,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.inducedOuterMeasure_eq' | [] | [
1472,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1471,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_neBot_of_mem | [] | [
400,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.map_map | [] | [
446,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.findGreatest_of_not | [
{
"state_after": "no goals",
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"tactic": "simp [Nat.findGreatest, h]"
}
] | [
903,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.forall_congr_left' | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
912,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
11
] |
Mathlib/Algebra/Lie/UniversalEnveloping.lean | UniversalEnvelopingAlgebra.lift_symm_apply | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.xor_self | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ xor b b = false",
"tactic": "cases b <;> simp"
}
] | [
49,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.eq_of_irreducible | [
{
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"state_before": "A : Type u_2\nB : Type... | [
129,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.is_left_invariant_chaar | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\ng : G\nK : Compacts G\neval : (Compacts G → ℝ) → ℝ := fun f => f (Compacts.map (fun b => g * b) (_ : Continuous fun b => g * b) K) - f K\n⊢ chaar K₀ (Compacts.map (fun b => g * b) ... | [
532,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.parts_top_subsingleton | [] | [
266,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.decide_true | [] | [
128,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.UniformIntegrable.memℒp | [] | [
95,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.inter_eq_of_inter_eq_of_eqOn | [
{
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463,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_induction' | [
{
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128,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Topology/Constructions.lean | Filter.Eventually.curry_nhds | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.40439\nδ : Type ?u.40442\nε : Type ?u.40445\nζ : Type ?u.40448\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\np : α × β → Prop\nx :... | [
598,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendsto_prod_filter_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nc : β\n⊢ Tendsto (Prod.mk c ∘ ↿F) (p ×ˢ p') (𝓤 β) ↔ TendstoUniformlyOnFilter F (fun x => c) p p'",
"state_before": "α : Type u\nβ ... | [
328,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/GroupTheory/Transfer.lean | MonoidHom.transfer_eq_pow_aux | [
{
"state_after": "case pos\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\nA : Type ?u.255305\ninst✝ : CommGroup A\nϕ : { x // x ∈ H } →* A\nT : ↑(leftTransversals ↑H)\ng : G\nkey : ∀ (k : ℕ) (g₀ : G), g₀⁻¹ * g ^ k * g₀ ∈ H → g₀⁻¹ * g ^ k * g₀ = g ^ k\nhH : index H = 0\n⊢ g ^ index H ∈ H\n\ncase neg\nG : Type ... | [
170,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_const' | [] | [
423,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.pairFunction_right | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.denselyOrdered_iff | [
{
"state_after": "case intro.inl.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.17805\nδ : Type ?u.17808\ninst✝¹ : LT α\ninst✝ : LT β\nx✝ : DenselyOrdered (α ⊕ β)\na b : α\nh : a < b\nc : α\nha : inl a < inl c\nhb : inl c < inl b\n⊢ ∃ a_1, a < a_1 ∧ a_1 < b\n\ncase intro.inr.intro\nα : Type u_1\nβ : Type u_2\nγ... | [
280,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Set/Function.lean | Function.update_comp_eq_of_not_mem_range' | [] | [
1681,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essSup_eq_sInf | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nm✝ : MeasurableSpace α\nμ✝ ν : MeasureTheory.Measure α\ninst✝ : ConditionallyCompleteLinearOrder β\nx : β\nf✝ : α → β\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf : α → β\n⊢ sInf {a | ∀ᶠ (n : β) in map f (Measure.ae μ), n ≤ a} = sInf {a | ↑↑μ {x | a < f x}... | [
94,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.dualBasis_repr | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : DecidableEq ι\nb : Basis ι R M\ninst✝ : _root_.Finite ι\nl : Dual R M\ni : ι\n⊢ ↑(↑(dualBasis b).repr l) i = ↑l (↑b i)",
... | [
439,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.antisymm | [] | [
447,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.one_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ninst✝ : NeZero n\n⊢ 1 = 0 ↔ n = 1",
"tactic": "rw [eq_comm, zero_eq_one_iff]"
}
] | [
858,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.foldl_induction | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nas : Array α\nmotive : Nat → β → Prop\ninit : β\nh0 : motive 0 init\nf : β → α → β\nhf : ∀ (i : Fin (size as)) (b : β), motive i.val b → motive (i.val + 1) (f b as[i])\nthis :\n (∀ (i : Fin (size as)) (b : β), motive i.val b → SatisfiesM (motive (i.val + 1)) (f b a... | [
124,
16
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
118,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.IsHaarMeasure.smul | [] | [
731,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.prevn | [
{
"state_after": "no goals",
"state_before": "l m₂ r m₁ : List Char\nx✝¹ : Substring\nx✝ : ValidFor l (List.reverse m₁ ++ m₂) r x✝¹\n⊢ Substring.prevn x✝¹ 0 { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len (List.drop 0 m₁) }",
"tactic": "simp [Substring.prevn]"
},
{
"state_after": "l m₂ r m₁ : L... | [
877,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
868,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Faithful.div_comp | [
{
"state_after": "case mk\nC : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nE : Type u₃\ninst✝² : Category E\nF F' : C ⥤ D\nG✝ G : D ⥤ E\ninst✝¹ : Faithful G\nobj : C → D\nmap : {X Y : C} → (X ⟶ Y) → (obj X ⟶ obj Y)\nF_pre : C ⥤q E\nmap_id✝ : ∀ (X : C), F_pre.map (𝟙 X) = 𝟙 (F_pre.obj X)\nma... | [
367,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.equiv_mk0 | [
{
"state_after": "R : Type u_1\nK : Type u_2\nL : Type ?u.1295805\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : DecidableEq L\ninst✝⁷ : Algebra R K\ninst✝⁶ : IsFractionRing R K\ninst✝⁵ : Algebra K L\ninst✝⁴ : FiniteDimensional K L\ninst✝³ : Algebra R L\ninst✝² : IsScalarTower R K L\ninst✝... | [
277,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_top_of_discrete | [] | [
68,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_ne_zero | [] | [
1242,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_univ | [] | [
2010,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2009,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.prob_le_one | [] | [
3225,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3224,
1
] |
Mathlib/Topology/Basic.lean | interior_subset_closure | [] | [
542,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_nat_cast | [] | [
358,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
11
] |
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