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/Combinatorics/SimpleGraph/Density.lean | Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul | [
{
"state_after": "case inl\n𝕜 : Type u_3\nι : Type ?u.73664\nκ : Type ?u.73667\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns s₁ s₂ : Finset α\nt t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\nhs : s₂ ⊆ s₁\nht : t₂ ⊆ t₁\nhδ : 0 ≤ δ\nhscard : (1 ... | [
260,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/List/Cycle.lean | List.next_singleton | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | LinearMap.toBilin_symm | [] | [
510,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Algebra/Module/Basic.lean | RingHom.smul_def | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.epi_inl_of_is_pushout_of_epi | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW✝ X Y Z : C\nf : X ⟶ Y\ng : X ⟶ Z\nt : PushoutCocone f g\nht : IsColimit t\ninst✝ : Epi g\nW : C\nh k : t.pt ⟶ W\ni : inl t ≫ h = inl t ≫ k\n⊢ inr t ≫ h = inr t ≫ k",
"tactic": "simp [← canc... | [
916,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ico | [] | [
206,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_pair | [
{
"state_after": "no goals",
"state_before": "x y : ZFSet\n⊢ toSet (pair x y) = {{x}, {x, y}}",
"tactic": "simp [pair]"
}
] | [
1291,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1291,
1
] |
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.IsClosable.graph_closure_eq_closure_graph | [
{
"state_after": "R : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module R E\ninst✝⁷ : Module R F\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : ContinuousAdd E\ninst✝³ : ContinuousAdd F\ninst✝² : TopologicalSpace R... | [
124,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Submodule.finrank_add_le_finrank_add_finrank | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\ns t : Submodule K V\ninst✝¹ : FiniteDimensional K { x // x ∈ s }\ninst✝ : FiniteDimensional K { x // x ∈ t }\n⊢ finrank K { x // x ∈ s ⊔ t } ≤ finrank K { x // x ∈ s ⊔ t } + finrank K { x // x ∈ s ⊓ ... | [
788,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/CategoryTheory/Bicategory/NaturalTransformation.lean | CategoryTheory.OplaxNatTrans.whiskerLeft_naturality_naturality | [
{
"state_after": "no goals",
"state_before": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G H : OplaxFunctor B C\nη : OplaxNatTrans F G\nθ : OplaxNatTrans G H\na b c : B\na' : C\nf : a' ⟶ (↑G.toPrelaxFunctor).obj a\ng h : a ⟶ b\nβ : g ⟶ h\n⊢ f ◁ PrelaxFunctor.map₂ G.toPrelaxFunc... | [
114,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.length_le | [
{
"state_after": "n : ℕ\nc : Composition n\n⊢ length c ≤ sum c.blocks",
"state_before": "n : ℕ\nc : Composition n\n⊢ length c ≤ n",
"tactic": "conv_rhs => rw [← c.blocks_sum]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nc : Composition n\n⊢ length c ≤ sum c.blocks",
"tactic":... | [
203,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_natDegree | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Real.continuousAt_const_rpow' | [
{
"state_after": "a b : ℝ\nh : b ≠ 0\nthis : rpow a = fun x => (↑a ^ ↑x).re\n⊢ ContinuousAt (rpow a) b",
"state_before": "a b : ℝ\nh : b ≠ 0\n⊢ ContinuousAt (rpow a) b",
"tactic": "have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by\n ext1 x\n rw [rpow_eq_pow, rpow_def]"
},
{
"state_afte... | [
199,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.countp_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.308016\nγ : Type ?u.308019\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidableEq α\ns t : Multiset α\nh : t ≤ s\n⊢ countp p (s - t) = countp p s - countp p t",
"tactic": "simp [countp_eq_card_filter, h, filter_le_filter]"
}... | [
2263,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2261,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.IsSwap.of_subtype_isSwap | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\np : α → Prop\ninst✝ : DecidablePred p\nf : Perm (Subtype p)\nh : IsSwap f\nx : α\nhx : p x\ny : α\nhy : p y\nhxy : ¬x = y ∧ f = swap { val := x, property := hx } { val := y, property := hy }\n⊢ x ≠ y",
"state_before": "α : Type u_1\ninst✝¹ : DecidableE... | [
241,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Topology/Instances/Rat.lean | Int.dist_cast_rat | [
{
"state_after": "x y : ℤ\n⊢ dist ↑↑x ↑↑y = dist ↑x ↑y",
"state_before": "x y : ℤ\n⊢ dist ↑x ↑y = dist x y",
"tactic": "rw [← Int.dist_cast_real, ← Rat.dist_cast]"
},
{
"state_after": "no goals",
"state_before": "x y : ℤ\n⊢ dist ↑↑x ↑↑y = dist ↑x ↑y",
"tactic": "congr"
}
] | [
76,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_biUnion_lt_top | [
{
"state_after": "case h.e'_3.h.e'_3.h.e'_3\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.25458\nδ : Type ?u.25461\nι : Type ?u.25464\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ns : Set β\nf : β → Set α\nhs : Set.Finite s\nhfin : ∀ (i : β), i ∈ s → ↑↑μ (f i) ≠ ⊤\n⊢ (fun i => ⋃ (_ : i ∈ s), f... | [
263,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.hasSum_real_toNNReal_of_nonneg | [] | [
166,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/BoundedOrder.lean | sup_bot_eq | [] | [
477,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.rotateR_nil | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.sign_neg | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ↑sign (-↑x) = -↑sign ↑x",
"tactic": "rw [← coe_neg, sign_coe, sign_coe, Left.sign_neg]"
}
] | [
1127,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_ccosh | [] | [
477,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_σ_self | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ X.map (SimplexCategory.σ i).op ≫ X.map (SimplexCategory.δ (↑Fin.castSucc i)).op = 𝟙 (X.obj [n].op)",
"state_before": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ σ X i ≫... | [
159,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Set/Sups.lean | Set.Nonempty.infs | [] | [
275,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
11
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_mul_distrib | [] | [
676,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_C | [] | [
812,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.tendsto_eval_ae_ae | [] | [
456,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.U_two | [
{
"state_after": "R : Type u_1\nS : Type ?u.9628\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ 2 * X * (2 * X) - 1 = 4 * X ^ 2 - 1",
"state_before": "R : Type u_1\nS : Type ?u.9628\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ U R 2 = 4 * X ^ 2 - 1",
"tactic": "simp only [U]"
},
{
"state_after": "no... | [
118,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBy_isTorsionBy | [] | [
362,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_sum | [] | [
1119,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.eq_univ_of_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7801\nγ : Type ?u.7804\ninst✝ : Fintype α\ns : Finset α\nhs : card s = Fintype.card α\n⊢ card univ ≤ card s",
"tactic": "rw [hs, Finset.card_univ]"
}
] | [
256,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm : OuterMeasure α\ns s₁ s₂ : Set α\n⊢ IsCaratheodory m ∅",
"tactic": "simp [IsCaratheodory, m.empty, diff_empty]"
}
] | [
954,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_alternating_of_le_neg_one | [
{
"state_after": "α : Type u\nβ : Type ?u.231983\nn✝ : ℕ\nx : α\ninst✝ : StrictOrderedRing α\nhx : x + 1 ≤ 0\nn : ℕ\nhx0 : x ≤ 0\n⊢ if Even n then ∑ i in range n, x ^ i ≤ 0 else 1 ≤ ∑ i in range n, x ^ i",
"state_before": "α : Type u\nβ : Type ?u.231983\nn✝ : ℕ\nx : α\ninst✝ : StrictOrderedRing α\nhx : x + ... | [
484,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Topology/Constructions.lean | tendsto_subtype_rng | [
{
"state_after": "α : Type u\nβ✝ : Type v\nγ : Type ?u.159970\nδ : Type ?u.159973\nε : Type ?u.159976\nζ : Type ?u.159979\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β✝\ninst✝ : TopologicalSpace γ\np✝ : α → Prop\nβ : Type u_1\np : α → Prop\nb : Filter β\nf : β → Subtype p\na : α\nha : p a\n⊢ Tendsto... | [
1081,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/Topology/Basic.lean | mem_interior | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\nx : α\n⊢ x ∈ interior s ↔ ∃ t, t ⊆ s ∧ IsOpen t ∧ x ∈ t",
"tactic": "simp only [interior, mem_sUnion, mem_setOf_eq, and_assoc, and_left_... | [
285,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | Measurable.exists_continuous | [
{
"state_after": "case intro.intro.intro\nα✝ : Type ?u.65771\ninst✝⁶ : TopologicalSpace α✝\nι : Type ?u.65777\nα : Type u_1\nβ : Type u_2\nt : TopologicalSpace α\ninst✝⁵ : PolishSpace α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : BorelSpace α\ntβ : TopologicalSpace β\ninst✝² : SecondCountableTopology β\ninst✝¹ : Meas... | [
262,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/List/Zip.lean | List.map_zipWith | [
{
"state_after": "case nil\nα : Type u\nβ : Type u_3\nγ : Type u_2\nδ✝ : Type ?u.62572\nε : Type ?u.62575\nδ : Type u_1\nf : α → β\ng : γ → δ → α\nl'✝ l' : List δ\n⊢ map f (zipWith g [] l') = zipWith (fun x y => f (g x y)) [] l'\n\ncase cons\nα : Type u\nβ : Type u_3\nγ : Type u_2\nδ✝ : Type ?u.62572\nε : Type ... | [
170,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_one | [] | [
126,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
125,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_sub_st | [] | [
732,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.map_desc | [
{
"state_after": "case w\nJ : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF : J ⥤ C\ninst✝ : HasColimitsOfShape J C\nG : J ⥤ C\nα : F ⟶ G\nc : Cocone G\n⊢ ∀ (j : J), ι F j ≫ colimMap α ≫ desc G c = ι F j ≫ desc F ((Cocones.precompose α).obj c)",
"state_be... | [
1112,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1109,
1
] |
Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.sup_support_finset_prod_le | [] | [
165,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.not_exists_sq' | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nhl : m ^ 2 < n\nhr : n < (m + 1) ^ 2\n⊢ ¬∃ t, t ^ 2 = n",
"tactic": "simpa only [pow_two] using\n not_exists_sq (by simpa only [pow_two] using hl) (by simpa only [pow_two] using hr)"
},
{
"state_after": "no goals",
"state_before": "n m ... | [
209,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.range_one | [] | [
2672,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2671,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.toFun_eq_coe | [] | [
353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_lt_of_one_lt' | [] | [
702,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.cons_dotProduct_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : AddCommMonoid α\ninst✝ : Mul α\nx : α\nv : Fin n → α\ny : α\nw : Fin n → α\n⊢ vecCons x v ⬝ᵥ vecCons y w = x * y + v ⬝ᵥ w",
"tactic": "simp"
}
] | [
160,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_gt_Icc | [] | [
258,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Computability/Reduce.lean | reflexive_manyOneReducible | [] | [
69,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_iInf_finite' | [] | [
855,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.coe_nat_pos | [] | [
44,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.has_union | [
{
"state_after": "α : Type u_1\nd : DynkinSystem α\ns₁ s₂ : Set α\nh₁ : Has d s₁\nh₂ : Has d s₂\nh : Disjoint s₁ s₂\n⊢ Has d (⋃ (b : Bool), bif b then s₁ else s₂)",
"state_before": "α : Type u_1\nd : DynkinSystem α\ns₁ s₂ : Set α\nh₁ : Has d s₁\nh₂ : Has d s₂\nh : Disjoint s₁ s₂\n⊢ Has d (s₁ ∪ s₂)",
"ta... | [
587,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.vector_toList | [] | [
1285,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
] |
Mathlib/Analysis/SpecialFunctions/Sqrt.lean | HasDerivWithinAt.sqrt | [] | [
86,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_E'5 | [] | [
147,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.continuousWithinAt_primitive | [
{
"state_after": "case pos\nι : Type ?u.18098281\n𝕜 : Type ?u.18098284\nE : Type u_1\nF : Type ?u.18098290\nA : Type ?u.18098293\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b b₀ b₁ b₂ : ℝ\nμ : MeasureTheory.Measure ℝ\nf g : ℝ → E\nhb₀ : ↑↑μ {b₀} = 0\nh_int : IntervalInt... | [
1192,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.296683\nG : Type ?u.296686\n𝕜 : Type ?u.296689\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
499,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.monotone_filter_left | [] | [
2732,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2732,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_pos | [] | [
353,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
20
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_sum_finset | [] | [
650,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.tan_sq_div_one_add_tan_sq | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\nhx : cos x ≠ 0\n⊢ tan x ^ 2 / (1 + tan x ^ 2) = sin x ^ 2",
"tactic": "simp only [← tan_mul_cos hx, mul_pow, ← inv_one_add_tan_sq hx, div_eq_mul_inv, one_mul]"
}
] | [
1320,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_le_of_liminf_slope_right_lt_deriv_boundary | [] | [
147,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.refl_trans | [] | [
366,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Std/Data/List/Basic.lean | List.leftpad_eq_leftpadTR | [
{
"state_after": "case h.h.h.h\nα : Type u_1\nn : Nat\na : α\nl : List α\n⊢ leftpad n a l = leftpadTR n a l",
"state_before": "⊢ @leftpad = @leftpadTR",
"tactic": "funext α n a l"
},
{
"state_after": "no goals",
"state_before": "case h.h.h.h\nα : Type u_1\nn : Nat\na : α\nl : List α\n⊢ leftp... | [
621,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
620,
10
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.omega_isLimit | [
{
"state_after": "o : Ordinal\nh : o < ω\nn : ℕ\ne : o = ↑n\n⊢ succ o < ω",
"state_before": "o : Ordinal\nh : o < ω\n⊢ succ o < ω",
"tactic": "let ⟨n, e⟩ := lt_omega.1 h"
},
{
"state_after": "o : Ordinal\nh : o < ω\nn : ℕ\ne : o = ↑n\n⊢ succ ↑n < ω",
"state_before": "o : Ordinal\nh : o < ω\n... | [
2426,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2423,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_weightedVSubVSubWeights | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV : Type u_2\nP : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.453666\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\np : ι → P\ni j : ι\nhi : i ∈ s\nhj : j ∈ s\n⊢ ↑(... | [
762,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.lift_of | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nM : ι → Type u_2\ninst✝² : (i : ι) → Monoid (M i)\nN✝ : Type ?u.134151\ninst✝¹ : Monoid N✝\nN : Type u_1\ninst✝ : Monoid N\nfi : (i : ι) → M i →* N\ni : ι\nm : M i\n⊢ ↑(↑lift fi) (↑of m) = ↑(fi i) m",
"tactic": "conv_rhs => rw [← lift.symm_appl... | [
168,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Group/Opposite.lean | AddOpposite.opMulEquiv_toEquiv | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.map_id | [] | [
609,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.range_finite | [
{
"state_after": "X : Type u_1\nY : Type u_2\nZ : Type ?u.6330\nα : Type ?u.6333\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nf : X → Y\nhf : IsLocallyConstant f\nthis : TopologicalSpace Y := ⊥\n⊢ Set.Finite (range f)",
"state_before": "X : Type u_1\nY : Type u_2\nZ : Type ?u.6330\nα : Type ?u.6333... | [
189,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.prod | [] | [
546,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\n𝓟 : Ideal R\nf : R[X]\nhf : IsWeaklyEisensteinAt f 𝓟\nS : Type v\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\nx : R\nhroot : IsRoot f x\nhmo : Monic f\ni : ℕ\nhi : natDegree f ≤ i\n⊢ x ^ i ∈ 𝓟",
"state_before": "R : Type u\ninst✝² : CommRing R\n𝓟 : Ideal ... | [
142,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_sub_nat_mul_pi | [] | [
1043,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopy.trans_apply | [] | [
137,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.le_def | [] | [
349,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mem_prod_list_ofFn | [
{
"state_after": "F : Type ?u.406111\nα : Type u_1\nβ : Type ?u.406117\nγ : Type ?u.406120\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid α\ns✝ t : Finset α\na✝ : α\nm n : ℕ\na : α\ns : Fin n → Finset α\n⊢ (∃ f, List.prod (List.ofFn fun i => ↑(f i)) = a) ↔ ∃ f, List.prod (List.ofFn fun i => ↑(f... | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_sub | [] | [
605,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
11
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_monomial_one_add_sub | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\nx : R\ninst✝ : CommRing S\nd : ℕ\ny : S\ncast_succ : ↑d + 1 = ↑(Nat.succ d)\n⊢ eval (1 + y) (↑(monomial d) (↑d + 1)) - eval y (↑(monomial d) (↑d + 1)) =\n ∑ x_1 in range (d + 1), ↑(Nat.choos... | [
434,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.extension_map | [
{
"state_after": "α : Type u_3\ninst✝⁴ : UniformSpace α\nβ : Type u_2\ninst✝³ : UniformSpace β\nγ : Type u_1\ninst✝² : UniformSpace γ\nf✝ : α → β\ninst✝¹ : CompleteSpace γ\ninst✝ : SeparatedSpace γ\nf : β → γ\ng : α → β\nhf : UniformContinuous f\nhg : UniformContinuous g\na : α\n⊢ (Completion.extension f ∘ Comp... | [
620,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Algebra/AddTorsor.lean | AddTorsor.subsingleton_iff | [
{
"state_after": "G : Type u_1\nP : Type u_2\ninst✝¹ : AddGroup G\ninst✝ : AddTorsor G P\ninhabited_h : Inhabited P\n⊢ Subsingleton G ↔ Subsingleton P",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝¹ : AddGroup G\ninst✝ : AddTorsor G P\n⊢ Subsingleton G ↔ Subsingleton P",
"tactic": "inhabit P"
},... | [
492,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/CategoryTheory/Subobject/Comma.lean | CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nS : C ⥤ D\nT : D\nA : CostructuredArrow S T\nP : (CostructuredArrow S T)ᵒᵖ\nf : P ⟶ A.op\ninst✝ : Mono f.unop.left.op\n⊢ f.unop.left.op.unop ≫ (Subobject.underlyingIso f.unop.left.op).hom.unop =\n (Subobject.arrow (Subobjec... | [
178,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.apply_symm_apply | [] | [
743,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/Order/Bounds/Basic.lean | BddAbove.exists_ge | [] | [
496,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDerivWithin_add_apply | [] | [
1229,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.get?_nil | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_mul | [
{
"state_after": "x y z : ℂ\nh₁ : -π < (log x * y).im\nh₂ : (log x * y).im ≤ π\n⊢ (if x = 0 then if y * z = 0 then 1 else 0 else exp (log x * (y * z))) =\n if (if x = 0 then if y = 0 then 1 else 0 else exp (log x * y)) = 0 then if z = 0 then 1 else 0\n else exp (log (if x = 0 then if y = 0 then 1 else 0 e... | [
102,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Set/Function.lean | Set.maps_range_to | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type u_3\nι : Sort ?u.23873\nπ : α → Type ?u.23878\ns✝ s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf✝ f₁ f₂ f₃ : α → β\ng✝ g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nf : α → β\ng : γ → α\ns : Set β\n⊢ MapsTo f (ra... | [
533,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.runK_lift | [] | [
59,
158
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
59,
9
] |
Mathlib/Order/PrimeIdeal.lean | Order.Ideal.isPrime_iff_mem_or_compl_mem | [] | [
197,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.uniqueFactorizationMonoid_of_fintype | [
{
"state_after": "case zero\nR : Type u\nS : Type ?u.1021136\nσ : Type v\nM : Type w\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nD : Type u\ninst✝³ : CommRing D\ninst✝² : IsDomain D\ninst✝¹ : UniqueFactorizationMonoid D\nd : ℕ\ninst✝ : Fintype σ\n⊢ UniqueFactorizatio... | [
1245,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
9
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_fin_one | [] | [
792,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostFun_mul | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nS : Type ?u.727613\nT : Type ?u.727616\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.727631\nβ : Type ?u.727634\nx y : 𝕎 R\n⊢ WittVector.ghostFun (x * y) = WittVector.ghostFun x * WittVe... | [
207,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
9
] |
Mathlib/Data/Finset/Sups.lean | Finset.singleton_infs_singleton | [] | [
334,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Functor.map_inv | [
{
"state_after": "case hom_inv_id\nC : Type u\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso f\n⊢ F.map f ≫ F.map (inv f) = 𝟙 (F.obj X)",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nF : C... | [
624,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.104853\nR : Type ?u.104856\nR' : Type ?u.104859\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\ns : Set α\n⊢ ↑(↑(restrict ∅) m) s = ↑0 s",
"tactic": "simp"
}
] | [
585,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.moveLeft | [] | [
268,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Sheaves/PresheafOfFunctions.lean | TopCat.presheafToTypes_map | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/EpiMono.lean | CategoryTheory.preserves_epi_of_preservesColimit | [
{
"state_after": "C : Type u₁\nD : Type u₂\ninst✝³ : Category C\ninst✝² : Category D\nF : C ⥤ D\nX Y : C\nf : X ⟶ Y\ninst✝¹ : PreservesColimit (span f f) F\ninst✝ : Epi f\nthis : IsColimit (PushoutCocone.mk (F.map (𝟙 Y)) (F.map (𝟙 Y)) (_ : F.map f ≫ F.map (𝟙 Y) = F.map f ≫ F.map (𝟙 Y)))\n⊢ Epi (F.map f)",
... | [
66,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_min_max | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.11464703\n𝕜 : Type ?u.11464706\nE : Type u_1\nF : Type ?u.11464712\nA : Type ?u.11464715\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf✝ g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nf : ℝ → E\n⊢ ‖∫ (x : ℝ) i... | [
530,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_neg | [] | [
506,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffOn.uniqueDiffWithinAt | [] | [
265,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
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