file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Intervals/Monotone.lean | monotone_Iio | [] | [
37,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.conj_comp | [] | [
2385,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2383,
1
] |
Mathlib/Order/WithBot.lean | WithTop.le_ofDual_iff | [] | [
818,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | smul_unitBall | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nhc : c ≠ 0\n⊢ c • ball 0 1 = ball 0 ‖c‖",
"tactic": "rw [_root_.smul_ball hc, smul_zero, mul_one]"
}
] | [
98,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.FG.of_map_embedding | [
{
"state_after": "case intro\nL : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nf : M ↪[L] N\ns : Substructure L M\nt : Finset N\nh : LowerAdjoint.toFun (closure L) ↑t = Substructure.map (Embedding.toHom f) s\n⊢ FG s",
"state_before": "L : Language\nM : Type u_4\ninst✝... | [
101,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/List/Infix.lean | List.inits_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.38861\nl✝ l₁ l₂ l₃ : List α\na✝ b : α\nm n : ℕ\na : α\nl : List α\n⊢ inits (a :: l) = [] :: map (fun t => a :: t) (inits l)",
"tactic": "simp"
}
] | [
373,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | Finite.isField_of_domain | [
{
"state_after": "case intro\nR✝ : Type ?u.39609\nG : Type ?u.39612\ninst✝⁵ : Ring R✝\ninst✝⁴ : IsDomain R✝\ninst✝³ : Fintype R✝\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : Finite R\nval✝ : Fintype R\n⊢ IsField R",
"state_before": "R✝ : Type ?u.39609\nG : Type ?u.39612\ninst✝⁵ : Ring R✝... | [
116,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean | ContinuousLinearMap.measurable_apply | [] | [
62,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.SimpleFunc.exists_lt_lintegral_simpleFunc_of_lt_lintegral | [
{
"state_after": "case h_ind\nα : Type u_1\nβ : Type ?u.1832831\nγ : Type ?u.1832834\nδ : Type ?u.1832837\nm✝ m0 : MeasurableSpace α\nE : Type ?u.1832846\ninst✝³ : NormedAddCommGroup E\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : SigmaFinite μ\nf : ... | [
2084,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2032,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_pure | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.247658\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\nb : β\n⊢ comap m (pure b) = 𝓟 (m ⁻¹' {b})",
"tactic": "rw [← principal_singleton, comap_principal]"
}
... | [
2144,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2143,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Real.sin_eq_tsum | [] | [
122,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/Parity.lean | Odd.neg | [
{
"state_after": "case intro\nF : Type ?u.101923\nα : Type u_1\nβ : Type ?u.101929\nR : Type ?u.101932\ninst✝ : Ring α\na b : α\nn : ℕ\nk : α\nhk : a = 2 * k + 1\n⊢ Odd (-a)",
"state_before": "F : Type ?u.101923\nα : Type u_1\nβ : Type ?u.101929\nR : Type ?u.101932\ninst✝ : Ring α\na b : α\nn : ℕ\nhp : Odd ... | [
427,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\nhs : IsCompact s\nthis : CompactSpace ↑s\n⊢ TendstoLocallyUniformlyOn F f p s ↔ TendstoUniformlyOn F f p s... | [
711,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_one | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\n⊢ num 1 = 1",
"tactic": "convert num_div (1 : K[X]) 1 <;> simp"
}
] | [
1166,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1166,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasStrictFDerivAt.smul | [] | [
184,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.continuousAt | [] | [
864,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Energy.lean | Finpartition.energy_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ns : Finset α\nP : Finpartition s\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\n⊢ 0 ≤ energy P G",
"tactic": "refine' div_nonneg (Finset.sum_nonneg fun _ _ => sq_nonneg _) <| Nat.cast_nonneg _"
}
] | [
47,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/Set/Basic.lean | Subsingleton.set_cases | [] | [
2833,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2832,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.30556\nα : ι → Type u_2\nβ : ι → Type ?u.30566\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni j : ι\na : α i\n⊢ (¬∃ i, i ∈ s ∧ Set.Nonempty (t i)) ↔ ∀ (i : ι), i ∈ s → t i = ∅",
"tact... | [
225,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/List/NatAntidiagonal.lean | List.Nat.antidiagonal_succ' | [
{
"state_after": "n : ℕ\n⊢ map (fun i => (i, n + 1 - i)) (range n) ++ [(n, 1), (n + 1, 0)] =\n map (Prod.map id succ ∘ fun i => (i, n - i)) (range n) ++ [Prod.map id succ (n, 0), (n + 1, 0)]",
"state_before": "n : ℕ\n⊢ antidiagonal (n + 1) = map (Prod.map id succ) (antidiagonal n) ++ [(n + 1, 0)]",
"... | [
85,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_sub | [] | [
330,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_le_of_brange_subset | [
{
"state_after": "case intro.intro\nα : Type ?u.360714\nβ : Type ?u.360717\nγ : Type ?u.360720\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\no' : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\ng : (a : Ordinal) → a < o' → Ordinal\nh : brange o f ⊆ brange o' g\na : Ordinal\nx✝ : a ∈ brange o... | [
1934,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1929,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.image_coe_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ioc a b = Ioc ↑a ↑b",
"tactic": "rw [← preimage_coe_Ioc, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left (Subset.trans Ioc_subset_Ioi_self <| Ioi_subset_Ioi bot_le)]"
}
] | [
224,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_zpow | [
{
"state_after": "q : ℚ\nx y : ℝ\nn : ℕ\nh : Irrational (x ^ n)\n⊢ Irrational x",
"state_before": "q : ℚ\nx y : ℝ\nn : ℕ\nh : Irrational (x ^ ↑n)\n⊢ Irrational x",
"tactic": "rw [zpow_ofNat] at h"
},
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nn : ℕ\nh : Irrational (x ^ n)\... | [
490,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Data/PFun.lean | PFun.fixInduction_spec | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.31479\nδ : Type ?u.31482\nε : Type ?u.31485\nι : Type ?u.31488\nC : α → Sort u_1\nf : α →. β ⊕ α\nb : β\na : α\nh : b ∈ fix f a\nH : (a' : α) → b ∈ fix f a' → ((a'' : α) → Sum.inr a'' ∈ f a' → C a'') → C a'\n⊢ (let_fun h₂ :=\n (_ :\n b ∈\n ... | [
350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.coe_range_mem_nhds | [] | [
70,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.star_apply | [] | [
1473,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublists_reverse | [] | [
186,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.gradeBy.isInternal | [] | [
233,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.closedEmbedding | [] | [
336,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
11
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.smul_of_comm | [] | [
188,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/CategoryTheory/Adjunction/Comma.lean | CategoryTheory.nonempty_isLeftAdjoint_iff_hasTerminal_costructuredArrow | [] | [
187,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Dynamics/Minimal.lean | IsCompact.exists_finite_cover_smul | [] | [
101,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.coe_to_lieHom | [] | [
551,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_univ₂ | [
{
"state_after": "X : Type u\nα : Type v\ninst✝⁴ : TopologicalSpace X\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderClosedTopology α\ninst✝ : PreconnectedSpace X\na b : X\nf g : X → α\nhf : Continuous f\nhg : Continuous g\nha : f a ≤ g a\nhb : g b ≤ f b\n⊢ Set.Nonempty (univ ∩ {x | f x ≤ g... | [
74,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Category/Ring/Adjunctions.lean | CommRingCat.free_map_coe | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.int_add | [] | [
237,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.epi_of_epi_app | [
{
"state_after": "case w.h\nC : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF G H I : C ⥤ D\nα : F ⟶ G\ninst✝ : ∀ (X : C), Epi (α.app X)\nZ✝ : C ⥤ D\ng h : G ⟶ Z✝\neq : α ≫ g = α ≫ h\nX : C\n⊢ g.app X = h.app X",
"state_before": "C : Type u₁\ninst✝³ : Ca... | [
104,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_pow | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1300762\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1300768\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type ?u.1300780\nQ : Type ?u.1300783\nS : Type ?u.1300786\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMon... | [
1157,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparating_op_iff | [
{
"state_after": "case refine'_1\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\n𝒢 : Set C\nh𝒢 : IsSeparating (Set.op 𝒢)\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (G : C), G ∈ 𝒢 → ∀ (h : Y ⟶ G), f ≫ h = g ≫ h\n⊢ f = g\n\ncase refine'_2\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Categor... | [
100,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.monotone_gen | [] | [
85,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.le_sSup_image_Icc | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.75376\ninst✝⁷ : ConditionallyCompleteLinearOrder α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : DenselyOrdered α\ninst✝¹ : ConditionallyCompleteLinearOrder β\ninst✝ : OrderTopo... | [
452,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Set/Basic.lean | Set.isEmpty_coe_sort | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\n⊢ ¬IsEmpty ↑s ↔ ¬s = ∅",
"tactic": "simpa using nonempty_iff_ne_empty"
}
] | [
622,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.lt_top_iff_finite | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\n⊢ multiplicity a b < ⊤ ↔ Finite a b",
"tactic": "rw [lt_top_iff_ne_top, ne_top_iff_finite]"
}
] | [
222,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_iff_of_neg | [] | [
737,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.union_vsub | [] | [
1539,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Involutive.bijective | [] | [
902,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
11
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.tendsto_coe' | [] | [
111,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Icc_eq_Ioc | [] | [
1689,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1686,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.posPart_mk | [] | [
900,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/Data/Finset/Pairwise.lean | Finset.pairwiseDisjoint_range_singleton | [
{
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}... | [
33,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.mem_pow | [
{
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924,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.exists_pow_eq' | [
{
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251,
34
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242,
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Mathlib/Topology/ContinuousOn.lean | ContinuousOn.preimage_closed_of_closed | [
{
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.smul_apply | [] | [
620,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/Topology/Order/Basic.lean | eventually_le_nhds | [] | [
1191,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
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Mathlib/Data/Finset/Pointwise.lean | Finset.isUnit_iff | [
{
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.target_inter_inv_preimage_preimage | [] | [
302,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
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Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherianSpace_set_iff | [
{
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145,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.toMatrix'_comp | [
{
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1022,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioi_self | [] | [
530,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
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Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.diag_σ | [
{
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}
] | [
288,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
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Mathlib/Computability/TuringMachine.lean | Turing.TM1.stmts_trans | [
{
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"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nΛ : Type u_2\nσ : Type u_3\nM : Λ → ... | [
1365,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
1
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Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_mul_C_eq_of_mul_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : leadingCoeff p * a ≠ 0\n⊢ natDegree p ∈ support (p * ↑C a)",
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141,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Data/Set/Function.lean | Set.restrict_dite_compl | [] | [
93,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv | [] | [
338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Init/Data/Nat/Basic.lean | Nat.zero_lt_bit1 | [] | [
27,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
11
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.init_snoc | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (↑castSucc i)\ni✝ : Fin n\ny : α (↑castSucc i✝)\nz : α (last n)\ni : Fin n\n⊢ init (snoc p x) i = p i",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq : (i : F... | [
455,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
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Mathlib/Topology/Category/CompHaus/Basic.lean | CompHaus.coe_of | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Analysis/Convex/Jensen.lean | ConcaveOn.le_map_centerMass | [] | [
62,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
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Mathlib/LinearAlgebra/Dimension.lean | rank_span | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.418383\nR : Type u\ninst✝³ : Ring R\ninst✝² : StrongRankCondition R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nv : ι → M\nhv : LinearIndependent R v\nthis :... | [
863,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
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Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_Ioi | [] | [
424,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_of_le_one_of_le_of_nonneg | [] | [
821,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.21149\nβ : Type ?u.21152\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ ENNReal.ofReal 1 = 1",
"tactic": "simp [ENNReal.ofReal]"
}
] | [
245,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
9
] |
Mathlib/GroupTheory/Exponent.lean | card_dvd_exponent_pow_rank' | [] | [
387,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_le_comap_smul | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.2299921\nR₂ : Type ?u.2299924\nR₃ : Type ?u.2299927\nR₄ : Type ?u.2299930\nS : Type ?u.2299933\nK : Type ?u.2299936\nK₂ : Type ?u.2299939\nM : Type ?u.2299942\nM' : Type ?u.2299945\nM₁ : Type ?u.2299948\nM₂ : Type ?u.2299951\nM₃ : Type ?u.2299954\nM₄ : Type ?u.229995... | [
2544,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2539,
1
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Std/Data/Nat/Gcd.lean | Nat.gcd_mul_gcd_of_coprime_of_mul_eq_mul | [
{
"state_after": "case a\nc d a b : Nat\ncop : coprime c d\nh : a * b = c * d\n⊢ gcd a c * gcd b c ∣ c\n\ncase a\nc d a b : Nat\ncop : coprime c d\nh : a * b = c * d\n⊢ c ∣ gcd a c * gcd b c",
"state_before": "c d a b : Nat\ncop : coprime c d\nh : a * b = c * d\n⊢ gcd a c * gcd b c = c",
"tactic": "appl... | [
419,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
411,
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] |
Mathlib/CategoryTheory/Abelian/DiagramLemmas/Four.lean | CategoryTheory.Abelian.epi_of_epi_of_epi_of_mono | [
{
"state_after": "V : Type u\ninst✝¹ : Category V\ninst✝ : Abelian V\nA B C D A' B' C' D' : V\nf : A ⟶ B\ng : B ⟶ C\nh : C ⟶ D\nf' : A' ⟶ B'\ng' : B' ⟶ C'\nh' : C' ⟶ D'\nα : A ⟶ A'\nβ : B ⟶ B'\nγ : C ⟶ C'\nδ : D ⟶ D'\ncomm₁ : α ≫ f' = f ≫ β\ncomm₂ : β ≫ g' = g ≫ γ\ncomm₃ : γ ≫ h' = h ≫ δ\nhgh : Exact g h\nhf'g'... | [
185,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/Data/List/Sigma.lean | List.dlookup_kerase_ne | [
{
"state_after": "case nil\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nh : a ≠ a'\n⊢ dlookup a (kerase a' []) = dlookup a []\n\ncase cons\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nh : a ≠ a'\nhead✝ : Sigma β\ntail✝ : List ... | [
518,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
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Mathlib/Data/Rat/BigOperators.lean | Rat.cast_list_sum | [] | [
29,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_coe_le_of_lintegral_coe_le | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.1091665\nF : Type ?u.1091668\n𝕜 : Type ?u.1091671\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup... | [
1205,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_closure | [] | [
898,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Nat.frequently_atTop_iff_infinite | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.6949\nα : Type ?u.6952\nβ : Type ?u.6955\nl : Filter α\np : ℕ → Prop\n⊢ (∃ᶠ (n : ℕ) in atTop, p n) ↔ Set.Infinite {n | p n}",
"tactic": "rw [← Nat.cofinite_eq_atTop, frequently_cofinite_iff_infinite]"
}
] | [
155,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_sUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.16439\nγ : Type ?u.16442\nδ : Type ?u.16445\ninst✝ : TopologicalSpace α\nS : Set (Set α)\nhS : Set.Finite S\na : α\n⊢ 𝓝[⋃₀ S] a = ⨆ (s : Set α) (_ : s ∈ S), 𝓝[s] a",
"tactic": "rw [sUnion_eq_biUnion, nhdsWithin_biUnion hS]"
}
] | [
253,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_neg | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝ : Ring α\nI : Ideal α\na b x : α\n⊢ span {-x} = span {x}",
"tactic": "ext"
},
{
"state_after": "case h\nα : Type u\nβ : T... | [
679,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | Units.openEmbedding_val | [] | [
238,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Logic/Basic.lean | not_imp_comm | [] | [
266,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.map_comp | [] | [
625,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Data/PFun.lean | PFun.preimage_eq | [] | [
518,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_cons_of_mem | [] | [
49,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.coe_monoidHom | [] | [
344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Basic.lean | eq_iff_le_not_lt | [] | [
394,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_of_mem | [] | [
769,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineIndependent.affineSpan_image_finset_eq_of_le_of_card_eq_finrank_add_one | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\np : ι → P\nhi : AffineIndependent k p\ns : Finset ι\nsp : AffineSubspace k P\ninst✝ : FiniteDimensional k { x // x ∈ direction sp }\nhle : af... | [
245,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | nonempty_embedding_to_cardinal | [
{
"state_after": "α : Type ?u.58\nβ : Type ?u.61\nγ : Type ?u.64\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nσ : Type u\nx✝ : Nonempty (Cardinal ↪ σ)\nf : Cardinal → σ\nhf : Injective f\ng : σ → Cardinal := Function.invFun f\nx : σ\nhx : g x = 2 ^ sum g\nthis : g x ≤ sum g\n⊢ 2 ^ sum g > sum g",
... | [
88,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.zero_right | [
{
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{
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_iff_compact | [
{
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Mathlib/Data/Pi/Algebra.lean | Pi.pow_apply | [] | [
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderiv_const_smul | [] | [
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Mathlib/Data/Set/Intervals/Monotone.lean | StrictMonoOn.Iic_id_le | [
{
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