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/Order/Concept.lean | subset_intentClosure_iff_subset_extentClosure | [] | [
67,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.mem_toAddSubmonoid | [] | [
76,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_zero | [] | [
482,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.Perm.congr_arg | [] | [
138,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.nontrivial_toCycle | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : Perm α\nhf : IsCycle f\nx : α\nhx : ↑f x ≠ x\n⊢ Cycle.Nontrivial (toCycle f hf)",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nf : Perm α\nhf :... | [
425,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | infinite_not_isOfFinOrder | [
{
"state_after": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝ : LeftCancelMonoid G\nx : G\nh : ¬IsOfFinOrder x\ns : Set G := (fun n => x ^ n) '' {n | 0 < n}\n⊢ Set.Infinite {y | ¬IsOfFinOrder y}",
"state_before": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝ : LeftCancelMonoid G\n... | [
529,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.imp₂ | [] | [
92,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_le_limsup_of_le | [] | [
550,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.image_finset_prod | [] | [
57,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | Antitone.le_of_tendsto | [] | [
268,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.map_vadd | [] | [
97,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.HeapNode.realSize_toHeap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns✝ : HeapNode α\nn : Nat\nres : Heap α\na : α\nc s : HeapNode α\n⊢ Heap.realSize (toHeap.go (node a c s) n res) = realSize (node a c s) + Heap.realSize res",
"tactic": "simp [toHeap.go, go, Nat.add_assoc, Nat.add_left_comm]"
}
] | [
234,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
231,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_self | [] | [
404,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toMul_zero | [] | [
227,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Measure.integral_comp_smul | [
{
"state_after": "case inl\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : Complet... | [
85,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Group.rank_range_le | [] | [
419,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/CategoryTheory/Functor/Functorial.lean | CategoryTheory.map'_as_map | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.prod_eq_inf_comap | [] | [
485,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.left_le_of_le_inf_right | [] | [
391,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_closedBall' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.187348\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\n⊢ y ∈ closedBall x ε ↔ edist x y ≤ ε",
"tactic": "rw [edist_comm, mem_closedBall]"
}
] | [
545,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.Integrable.neg | [] | [
1232,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.sub_apply | [] | [
1255,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1254,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_prod_of_subset | [] | [
485,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/CategoryTheory/Products/Bifunctor.lean | CategoryTheory.Bifunctor.diagonal' | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝² : Category C\ninst✝¹ : Category D\ninst✝ : Category E\nF : C × D ⥤ E\nX X' : C\nf : X ⟶ X'\nY Y' : D\ng : Y ⟶ Y'\n⊢ F.map (f, 𝟙 Y) ≫ F.map (𝟙 X', g) = F.map (f, g)",
"tactic": "rw [← Functor.map_comp, prod_comp... | [
59,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.comap_comp | [] | [
382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
11
] |
Mathlib/LinearAlgebra/Determinant.lean | is_basis_iff_det | [
{
"state_after": "case mp\nR : Type u_2\ninst✝⁶ : CommRing R\nM : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type ?u.2551624\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\ne : Basis ι R M\nv : ι → M\n⊢ LinearIndependent R v ∧ span R (S... | [
567,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.IsPositive.conj_orthogonalProjection | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.262558\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : InnerProductSpace 𝕜 F\ninst✝² : CompleteSpace E\ninst✝¹ : CompleteSpace F\nU : Submodule 𝕜 E\nT : E →L[𝕜] E\nhT : IsPo... | [
112,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Std/Data/List/Lemmas.lean | List.reverse_infix | [
{
"state_after": "case refine_1\nα✝ : Type u_1\nl₁ l₂ : List α✝\nx✝ : reverse l₁ <:+: reverse l₂\ns t : List α✝\ne : s ++ reverse l₁ ++ t = reverse l₂\n⊢ reverse t ++ l₁ ++ reverse s = l₂\n\ncase refine_2\nα✝ : Type u_1\nl₁ l₂ : List α✝\nx✝ : l₁ <:+: l₂\ns t : List α✝\ne : s ++ l₁ ++ t = l₂\n⊢ reverse t ++ reve... | [
1629,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1625,
9
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimit.isoOfNatIso_hom_desc | [] | [
928,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.congr' | [] | [
354,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.coe_sort_coe | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.zmodRepr_lt_p | [] | [
208,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_positive | [] | [
578,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inclusion_mk | [] | [
2782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2781,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.pmap_res | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nl : Filter α\ns : Set α\nf : α → β\nt : Set β\n⊢ t ∈ pmap (PFun.res f s) l ↔ t ∈ map f (l ⊓ 𝓟 s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : Filter α\ns : Set α\nf : α → β\n⊢ pmap (PFun.res f s) l = map f (l ⊓ 𝓟 s)",
"tactic"... | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_eq | [] | [
164,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
162,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.coeFn_mono | [] | [
83,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_sub | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ cos (x - y) = cos x * cos y + sin x * sin y",
"tactic": "simp [sub_eq_add_neg, cos_add, sin_neg, cos_neg]"
}
] | [
1210,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
1
] |
Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformRight.card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Group α\ne : α\nx : Finset α × Finset α\n⊢ Finset.card x.snd + Finset.card (e⁻¹ • x.snd) = 2 * Finset.card x.snd",
"tactic": "rw [card_smul_finset, two_mul]"
}
] | [
170,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.forall_disjSups_iff | [
{
"state_after": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns s₁ s₂ t t₁ t₂ u : Finset α\na b c : α\np : α → Prop\n⊢ (∀ (c : α), (∃ a, a ∈ s ∧ ∃ b, b ∈ t ∧ Disjoint a b ∧ a ⊔ b = c) → p c) ↔\n ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ t → Dis... | [
471,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.prodIsoProd_inv_snd | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nX Y : TopCat\n⊢ (prodIsoProd X Y).inv ≫ prod.snd = prodSnd",
"tactic": "simp [Iso.inv_comp_eq]"
}
] | [
237,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | OpenEmbedding.compatiblePreserving | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nf : X ⟶ Y\nF : TopCat.Presheaf C Y\nhf : OpenEmbedding ((forget TopCat).map f)\nthis : Mono f\n⊢ CompatiblePreserving (Opens.grothendieckTopology ↑Y) (IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map f)))",
"state_before": "C : Type u\nins... | [
171,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/Minimal.lean | maximals_eq_minimals | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na b : α\ninst✝ : IsSymm α r\n⊢ maximals r s = minimals r s",
"tactic": "rw [minimals_of_symm, maximals_of_symm]"
}
] | [
118,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.mul_zero | [
{
"state_after": "no goals",
"state_before": "a : Rat\n⊢ a * 0 = 0",
"tactic": "simp [mul_def]"
}
] | [
261,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
261,
19
] |
Mathlib/Topology/MetricSpace/Basic.lean | NNReal.le_add_nndist | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.239808\nι : Type ?u.239811\ninst✝ : PseudoMetricSpace α\na b : ℝ≥0\n⊢ ↑a ≤ ↑b + dist a b",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.239808\nι : Type ?u.239811\ninst✝ : PseudoMetricSpace α\na b : ℝ≥0\n⊢ a ≤ b + nndist a b",
"tactic": "suff... | [
1706,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.splitAtPred_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl₁ : List α\no : α\nl₂ : List α\nx✝ : ∀ (x : α), x ∈ l₁ → p x = false\nleft✝ : p o = true\nh₃ : [] = l₁ ++ o :: l₂\n⊢ splitAtPred p [] = (l₁, some o, l₂)",
"tactic": "simp at h₃"
},
{
"state_after": "α : Type u_1\np : α → ... | [
1345,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_insert | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.20280\nδ : Type ?u.20283\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx : α\ny : β\n⊢ (x, y) ∈ s ×ˢ insert b t ↔ (x, y) ∈ (fun a => (a, b)) '' s ∪ s ×ˢ t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.20280\nδ : Type ?u.202... | [
196,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_lt | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.111454\nβ : Type ?u.111457\nγ : Type ?u.111460\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\n⊢ lift a < lift b ↔ a < b",
"tactic": "simp only [lt_iff_le_not_le, lift_le]"
}
] | [
778,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsAtomic.liftAt | [] | [
700,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.mod_eq_self_iff | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nhq0 : q ≠ 0\nh : degree p < degree q\nthis : ¬degree (q * ↑C (leadingCoeff q)⁻¹) ≤ degree p\n⊢ p % q = p",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : F... | [
238,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_le_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ b ≤ 1 * a ↔ b ≤ a",
"tactic": "rw [one_mul]"
}
] | [
271,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.comp₁ | [] | [
1437,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_nonempty_iff | [
{
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"tactic": "simp [Classical.skolem, Set.Nonempty]"
}
] | [
684,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_inf_distrib_right | [
{
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524,
28
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521,
1
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Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.neg_def | [] | [
351,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.add_inter_distrib | [
{
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"tactic": "rw [add_comm, inter_add_distrib, add_comm s, add_comm s]"
}
] | [
1876,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1875,
1
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Mathlib/Data/Rat/Cast.lean | Rat.cast_max | [] | [
358,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
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Mathlib/Data/Matrix/Basic.lean | Matrix.diag_multiset_sum | [] | [
693,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.top_adj | [] | [
381,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.tsupport_normed_eq | [
{
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541,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.Lifts.exists_upper_bound | [
{
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"state_before": "F : Type u... | [
1085,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_add_left | [
{
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248,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
11
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Mathlib/CategoryTheory/Abelian/DiagramLemmas/Four.lean | CategoryTheory.Abelian.isIso_of_isIso_of_isIso_of_isIso_of_isIso | [
{
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216,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/Data/Set/Pairwise/Lattice.lean | Set.pairwiseDisjoint_iUnion | [] | [
60,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
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Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_pow_self | [] | [
99,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Topology/FiberBundle/IsHomeomorphicTrivialBundle.lean | IsHomeomorphicTrivialFiberBundle.surjective_proj | [
{
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49,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/Data/Fin/Basic.lean | Fin.castPred_mk | [
{
"state_after": "n✝ m n i : ℕ\nh : i < n + 1\nthis : ¬↑castSucc (last n) < { val := i, isLt := (_ : i < Nat.succ (n + 1)) }\n⊢ castPred { val := i, isLt := (_ : i < Nat.succ (n + 1)) } = { val := i, isLt := h }",
"state_before": "n✝ m n i : ℕ\nh : i < n + 1\n⊢ castPred { val := i, isLt := (_ : i < Nat.succ... | [
2326,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2323,
1
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Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.isGLB_of_l_image | [] | [
845,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.tendsto_iff_tendstoUniformly | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.45029\nι : Type u_3\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\nF : ι → α →ᵤ β\nf : α →ᵤ β\n⊢ (∀ (i : Set (β × β)), i ∈ 𝓤 β → ∀ᶠ (x : ι) in p, F x ∈ {g | (f, g) ∈ UniformFun.gen α β i}) ↔\n ∀ (u : Set (β × β)), u ∈ 𝓤 β → ∀... | [
501,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
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Mathlib/Computability/Partrec.lean | Computable.fst | [] | [
305,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_lt_one' | [] | [
527,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
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Mathlib/Algebra/Category/GroupCat/Injective.lean | AddCommGroupCat.injective_of_injective_as_module | [
{
"state_after": "A : Type u\ninst✝¹ : AddCommGroup A\ninst✝ : Injective (ModuleCat.mk A)\nX Y : Bundled AddCommGroup\ng : X ⟶ Bundled.mk A\nf : X ⟶ Y\nm : Mono f\nG : ModuleCat.mk ↑X ⟶ ModuleCat.mk A :=\n {\n toAddHom :=\n { toFun := g.toFun,\n map_add' := (_ : ∀ (x y : ↑X), ZeroHom.toFun (↑g) ... | [
71,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
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Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.curry_injective | [] | [
241,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.toCompositionAsSet_blocks | [
{
"state_after": "n : ℕ\nc : Composition n\nd : CompositionAsSet n := toCompositionAsSet c\n⊢ CompositionAsSet.blocks (toCompositionAsSet c) = c.blocks",
"state_before": "n : ℕ\nc : Composition n\n⊢ CompositionAsSet.blocks (toCompositionAsSet c) = c.blocks",
"tactic": "let d := c.toCompositionAsSet"
}... | [
1037,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.tendsto_prod_self_iff | [
{
"state_after": "no goals",
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"tactic": "simp only [tend... | [
438,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivWithinAt.smul_const | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf✝ f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type u_1\ninst✝... | [
99,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Analysis/Complex/Basic.lean | Complex.imClm_apply | [] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.continuous_proj | [] | [
769,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
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] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.transnumAuxSeq_dist_lt | [
{
"state_after": "f g : CircleDeg1Lift\nn : ℕ\nthis : 0 < 2 ^ (n + 1)\n⊢ dist (transnumAuxSeq f n) (transnumAuxSeq f (n + 1)) < 1 / 2 / 2 ^ n",
"state_before": "f g : CircleDeg1Lift\nn : ℕ\n⊢ dist (transnumAuxSeq f n) (transnumAuxSeq f (n + 1)) < 1 / 2 / 2 ^ n",
"tactic": "have : 0 < (2 ^ (n + 1) : ℝ) :... | [
679,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_insert_adjoin | [] | [
230,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.ImageMap.map_uniq_aux | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\nf✝ g✝ : Arrow C\ninst✝³ : HasImage f✝.hom\ninst✝² : HasImage g✝.hom\nsq✝ : f✝ ⟶ g✝\nf g : Arrow C\ninst✝¹ : HasImage f.hom\ninst✝ : HasImage g.hom\nsq : f ⟶ g\nmap : image f.hom ⟶ image g.hom\nmap_ι : autoParam (map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right) _... | [
770,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Logic/Basic.lean | or_not_of_imp | [] | [
369,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Int/Dvd/Basic.lean | Int.coe_nat_dvd | [
{
"state_after": "m n : ℕ\nx✝ : ↑m ∣ ↑n\na : ℤ\nm0 : m = 0\nae : n = 0\n⊢ m ∣ n",
"state_before": "m n : ℕ\nx✝ : ↑m ∣ ↑n\na : ℤ\nae : ↑n = ↑m * a\nm0 : m = 0\n⊢ m ∣ n",
"tactic": "simp [m0] at ae"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\nx✝ : ↑m ∣ ↑n\na : ℤ\nm0 : m = 0\nae :... | [
34,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
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] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_sub_atTop_nat | [] | [
1654,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1653,
1
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Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_ge_three_eq_one | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ hyperoperation (n + 3) m 0 = 1",
"tactic": "rw [hyperoperation]"
}
] | [
55,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.fderivWithin | [
{
"state_after": "case none\n𝕜 : 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 ... | [
1190,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
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Mathlib/Data/Finset/Lattice.lean | Finset.le_sup_of_le | [] | [
125,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.mk_id | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/Analysis/NormedSpace/Exponential.lean | Function.update_exp | [
{
"state_after": "case h\n𝕂 : Type u_3\n𝔸✝ : Type ?u.766093\n𝔹 : Type ?u.766096\ninst✝¹⁰ : IsROrC 𝕂\ninst✝⁹ : NormedRing 𝔸✝\ninst✝⁸ : NormedAlgebra 𝕂 𝔸✝\ninst✝⁷ : NormedRing 𝔹\ninst✝⁶ : NormedAlgebra 𝕂 𝔹\ninst✝⁵ : CompleteSpace 𝔸✝\nι : Type u_1\n𝔸 : ι → Type u_2\ninst✝⁴ : Fintype ι\ninst✝³ : Decidab... | [
569,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.spanSingleton_inv | [] | [
153,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_left | [
{
"state_after": "no goals",
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302,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
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Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.ε_hom_inv_app | [] | [
110,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.is_left_invariant_prehaar | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nU : Set G\nhU : Set.Nonempty (interior U)\ng : G\nK : Compacts G\n⊢ prehaar (↑K₀) U (Compacts.map (fun b => g * b) (_ : Continuous fun b => g * b) K... | [
358,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/Computability/Reduce.lean | OneOneReducible.disjoin_right | [] | [
308,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.comp | [] | [
160,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Set/UnionLift.lean | Set.iUnionLift_const | [
{
"state_after": "α : Type u_1\nι : Sort u_3\nβ : Sort u_2\nS : ι → Set α\nf : (i : ι) → ↑(S i) → β\nhf :\n ∀ (i j : ι) (x : α) (hxi : x ∈ S i) (hxj : x ∈ S j),\n f i { val := x, property := hxi } = f j { val := x, property := hxj }\nT : Set α\nhT : T ⊆ iUnion S\nhT' : T = iUnion S\nc : ↑T\nci : (i : ι) → ↑... | [
103,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_one | [] | [
35,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.singleton_mul_subgroup | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.166670\nG : Type u_1\nA : Type ?u.166676\nS : Type ?u.166679\ninst✝³ : Group G\ninst✝² : AddGroup A\ns : Set G\ninst✝¹ : Group α\ninst✝ : MulDistribMulAction α G\nH : Subgroup G\nh : G\nhh : h ∈ H\nthis : {x | x ∈ H} = ↑H\n⊢ {h} * ↑H = ↑H",
"tact... | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_compl_iff | [] | [
1641,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
] |
Mathlib/Order/Hom/Basic.lean | Disjoint.map_orderIso | [
{
"state_after": "F : Type ?u.113997\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.114006\nδ : Type ?u.114009\ninst✝³ : SemilatticeInf α\ninst✝² : OrderBot α\ninst✝¹ : SemilatticeInf β\ninst✝ : OrderBot β\na b : α\nf : α ≃o β\nha : Disjoint a b\n⊢ ↑f (a ⊓ b) ≤ ↑f ⊥",
"state_before": "F : Type ?u.113997\nα : Type... | [
1212,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
1
] |
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