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 |
|---|---|---|---|---|---|---|
Std/Data/Int/Lemmas.lean | Int.natAbs_ne_zero | [] | [
149,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
149,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.one_im | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged | [] | [
262,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.comp_f | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | norm_iteratedFDerivWithin_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\... | [
793,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ioc | [] | [
517,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_neg | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.4480572\ninst✝ : IsROrC K\nz : K\n⊢ ↑normSq (-z) = ↑normSq z",
"tactic": "simp only [normSq_eq_def', norm_neg]"
}
] | [
498,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/CategoryTheory/Monoidal/Types/Basic.lean | CategoryTheory.leftUnitor_inv_apply | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.star'_quot | [] | [
566,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/List/MinMax.lean | List.not_lt_maximum_of_mem' | [
{
"state_after": "case none\nα : Type u_1\nβ : Type ?u.91154\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x < x_1\nl : List α\na m : α\nha : a ∈ l\nh : maximum l = none\n⊢ ¬none < ↑a\n\ncase some\nα : Type u_1\nβ : Type ?u.91154\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x < x_1\nl : Lis... | [
334,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.eq_div_of_mul_eq_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na b c : R\nha : a ≠ 0\nh : a * b = c\n⊢ b = c / a",
"tactic": "rw [← h, mul_div_cancel_left _ ha]"
}
] | [
99,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.pos | [] | [
70,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.add_isLittleO | [] | [
1087,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1086,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_rpow_iff | [] | [
433,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem | [] | [
203,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.prod_bot_sup_bot_prod | [] | [
929,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_fst_le | [] | [
138,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.unique_irreducible | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\nK : Type ?u.528557\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\ninst✝ : ValuationRing R\np q : R\nhp : Irreducible p\nhq : Irreducible q\nthis : p ∣ q ∨ q ∣ p\n⊢ Associated p q",
"state_before": "R : Type u_1\... | [
312,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.symm_trans_self | [] | [
452,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.preimage_mem_nhdsWithin' | [] | [
952,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullbackDiagonalMapIso_inv_snd_fst | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasPullbacks C\nU V₁ V₂ : C\nf : X ⟶ Y\ni : U ⟶ Y\ni₁ : V₁ ⟶ pullback f i\ni₂ : V₂ ⟶ pullback f i\ninst✝ : HasPullback i₁ i₂\n⊢ (Iso.mk (lift (snd ≫ fst) (snd ≫ snd) (_ : (snd ≫ fst) ≫ i₁ = (snd ≫ snd) ≫ i₂))\n (lift (fst ≫ i₁ ≫ f... | [
179,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/RingTheory/DedekindDomain/PID.lean | FractionalIdeal.isPrincipal.of_finite_maximals_of_inv | [
{
"state_after": "R : Type u_2\ninst✝³ : CommRing R\nA : Type u_1\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\nS : Submonoid R\ninst✝ : IsLocalization S A\nhS : S ≤ R⁰\nhf : Set.Finite {I | IsMaximal I}\nI I' : FractionalIdeal S A\nhinv hinv' : I * I' = 1\n⊢ Submodule.IsPrincipal ↑I",
"state_before": "R : Ty... | [
172,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.lie_apply | [] | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.dist_self | [
{
"state_after": "no goals",
"state_before": "E : ℕ → Type u_1\nx : (n : ℕ) → E n\n⊢ dist x x = 0",
"tactic": "simp [dist]"
}
] | [
280,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
11
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.firstDiff_comm | [
{
"state_after": "no goals",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\n⊢ firstDiff x y = firstDiff y x",
"tactic": "simp only [firstDiff_def, ne_comm]"
}
] | [
91,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/List/Basic.lean | List.tail_nil | [] | [
310,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
310,
9
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.pred | [
{
"state_after": "v : Vector ℕ (Nat.succ 0)\n⊢ Nat.rec 0 (fun y IH => y) (Vector.head v) = Nat.pred (Vector.head v)",
"state_before": "v : Vector ℕ (Nat.succ 0)\n⊢ Nat.rec 0 (fun y IH => Vector.head (y ::ᵥ IH ::ᵥ v)) (Vector.head v) = Nat.pred (Vector.head v)",
"tactic": "simp"
},
{
"state_after... | [
1451,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.sInf_def | [] | [
37,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.eq_last_of_not_lt | [] | [
549,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.filter_card_add_filter_neg_card_eq_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.42409\ns t : Finset α\nf : α → β\nn : ℕ\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : (x : α) → Decidable ¬p x\n⊢ card (filter p s) + card (filter (fun a => ¬p a) s) = card s",
"tactic": "classical rw [← card_union_eq (disjoint_f... | [
461,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrixAux_apply | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | SeminormedGroup.tendstoUniformlyOn_one | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.502213\n𝕜 : Type ?u.502216\nα : Type ?u.502219\nι : Type u_2\nκ : Type u_1\nE : Type ?u.502228\nF : Type ?u.502231\nG : Type u_3\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns✝ : Set E\na a₁ a₂ b b₁ b₂ : E\nr ... | [
1294,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.ker_quotient_lift | [
{
"state_after": "case h\nR : Type u\nS✝ : Type v\nF : Type w\ninst✝² : CommRing R\ninst✝¹ : CommRing S✝\nS : Type v\ninst✝ : CommRing S\nI : Ideal R\nf : R →+* S\nH : I ≤ RingHom.ker f\n⊢ ∀ (x : R ⧸ I), x ∈ RingHom.ker (Quotient.lift I f H) ↔ x ∈ map (Quotient.mk I) (RingHom.ker f)",
"state_before": "R : T... | [
129,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.sub_pf | [] | [
42,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.rightHom_eq_right | [] | [
185,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasStrictFDerivAt.exists_lipschitzOnWith | [] | [
457,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.zero_mem_center | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : MulZeroClass M\n⊢ 0 ∈ center M",
"tactic": "simp [mem_center_iff]"
}
] | [
59,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.map_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹³ : Ring R\nR₂ : Type u_2\ninst✝¹² : Ring R₂\nR₃ : Type ?u.715179\ninst✝¹¹ : Ring R₃\nM : Type u_3\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : AddCommGroup M\nM₂ : Type u_4\ninst✝⁸ : TopologicalSpace M₂\ninst✝⁷ : AddCommGroup M₂\nM₃ : Type ?u.715... | [
1299,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
11
] |
Mathlib/Algebra/Star/Module.lean | star_nat_cast_smul | [] | [
43,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sum.one_le_dist_inr_inl | [
{
"state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nx : X\ny : Y\n⊢ 1 ≤ Sum.dist (Sum.inl x) (Sum.inr y)",
"state_before": "X : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nx : X\ny : Y\n⊢ 1 ≤ Sum.dist (Sum.inr y) (Sum.inl x)... | [
227,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Topology/FiberBundle/IsHomeomorphicTrivialBundle.lean | IsHomeomorphicTrivialFiberBundle.isOpenMap_proj | [
{
"state_after": "case intro\nB : Type u_1\nF : Type u_2\nZ : Type u_3\ninst✝² : TopologicalSpace B\ninst✝¹ : TopologicalSpace F\ninst✝ : TopologicalSpace Z\ne : Z ≃ₜ B × F\nh : IsHomeomorphicTrivialFiberBundle F (Prod.fst ∘ ↑e)\n⊢ IsOpenMap (Prod.fst ∘ ↑e)",
"state_before": "B : Type u_1\nF : Type u_2\nZ :... | [
59,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
11
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.surjective_of_epi | [] | [
272,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Topology/Algebra/Order/ExtrClosure.lean | IsLocalMinOn.closure | [] | [
59,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
11
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.mapFun.int_cast | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_2\nS : Type u_1\nT : Type ?u.559389\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.559404\nβ : Type ?u.559407\nf : R →+* S\nx y : 𝕎 R\nn : ℤ\n⊢ mapFun (↑f) (Int.castDef n) = ↑n",
"tactic... | [
143,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.subset_union_prime' | [
{
"state_after": "R✝ : Type u\nι : Type u_1\ninst✝¹ : CommSemiring R✝\nI✝ J K L : Ideal R✝\nR : Type u\ninst✝ : CommRing R\ns : Finset ι\nf : ι → Ideal R\na b : ι\nhp : ∀ (i : ι), i ∈ s → IsPrime (f i)\nI : Ideal R\n⊢ (↑I ⊆ ↑(f a) ∪ ↑(f b) ∪ ⋃ (i : ι) (_ : i ∈ ↑s), ↑(f i)) → I ≤ f a ∨ I ≤ f b ∨ ∃ i, i ∈ s ∧ I ≤... | [
1196,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Topology/StoneCech.lean | ultrafilter_pure_injective | [
{
"state_after": "α : Type u\nx y : α\nh : pure x = pure y\n⊢ x = y",
"state_before": "α : Type u\n⊢ Function.Injective pure",
"tactic": "intro x y h"
},
{
"state_after": "α : Type u\nx y : α\nh : pure x = pure y\nthis : {x} ∈ pure x\n⊢ x = y",
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123,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_pure | [] | [
310,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_add | [
{
"state_after": "x y : ℝ\n⊢ ↑(sinh (x + y)) = ↑(sinh x * cosh y + cosh x * sinh y)",
"state_before": "x y : ℝ\n⊢ sinh (x + y) = sinh x * cosh y + cosh x * sinh y",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(sinh (x + y)) = ↑(sinh x * cosh y +... | [
1354,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1353,
8
] |
Mathlib/Data/Fin/Basic.lean | Fin.castAdd_castAdd | [
{
"state_after": "case h\nn✝ m✝ m n p : ℕ\ni : Fin m\n⊢ ↑(↑(castAdd p) (↑(castAdd n) i)) = ↑(↑(cast (_ : m + (n + p) = m + n + p)) (↑(castAdd (n + p)) i))",
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"tact... | [
1185,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_mul_Ioi_zero | [
{
"state_after": "no goals",
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"tactic": "erw [(Units.mk0 x hx.ne').mulLeft.image_eq_preimage, preimage_const_mul_Ioi 0 (inv_pos.m... | [
778,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_eq_zero | [
{
"state_after": "case nil\nι : Type ?u.107956\nα : Type ?u.107959\nM : Type ?u.107962\nN : Type ?u.107965\nP : Type ?u.107968\nM₀ : Type u_1\nG : Type ?u.107974\nR : Type ?u.107977\ninst✝ : MonoidWithZero M₀\nL : List M₀\nh✝ : 0 ∈ L\nh : 0 ∈ []\n⊢ prod [] = 0\n\ncase cons\nι : Type ?u.107956\nα : Type ?u.10795... | [
389,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_empty_of_one_mem | [] | [
221,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_mul_of_mem | [
{
"state_after": "ι : Type ?u.373499\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : α → β\na b : α\nha : a ∈ s\nhb : b ∈ s\nhn : a ≠ b\nh₀ : ∀ (c : α), c ∈ s → c ≠ a ∧ c ≠ b → f c = 1\nthis : DecidableEq α\n⊢ ∏ x in s, f x = f a * f b",
... | [
828,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
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Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Ico_iff_right | [] | [
89,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_nonneg | [
{
"state_after": "case zero\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nc : CU X\n⊢ 0 ≤ approx Nat.zero c x\n\ncase succ\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nn : ℕ\nihn : ∀ (c : CU X), 0 ≤ approx n c x\nc : CU X\n⊢ 0 ≤ appr... | [
162,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_add | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/Algebra/Tropical/BigOperators.lean | List.trop_sum | [
{
"state_after": "case nil\nR : Type u_1\nS : Type ?u.11\ninst✝ : AddMonoid R\n⊢ trop (sum []) = prod (map trop [])\n\ncase cons\nR : Type u_1\nS : Type ?u.11\ninst✝ : AddMonoid R\nhd : R\ntl : List R\nIH : trop (sum tl) = prod (map trop tl)\n⊢ trop (sum (hd :: tl)) = prod (map trop (hd :: tl))",
"state_bef... | [
48,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_curry | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type u_3\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : LocallyCompactSpace (α × β)\n⊢ Continuous (Function.uncurry fun x y => ↑(curry x) y)",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type u_3\... | [
387,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
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Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.add_def | [] | [
348,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_hom_comp | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF✝ : J ⥤ C\nt✝ : Cone F✝\nF G : J ⥤ C\ns : Cone F\nt : Cone G\nP : IsLimit s\nQ : IsLimit t\nw : F ≅ G\nj : J\n⊢ (conePointsIsoOfNatIso P Q w).hom ≫ t.π.app j = ... | [
317,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Mathlib/Data/Set/Function.lean | Set.MapsTo.coe_restrict | [] | [
371,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\n𝕜 : Type ?u.1622147\nE : Type u_1\nF : Type ?u.1622153\nA : Type ?u.1622156\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : CompleteSpace E\ninst✝² : NormedSpace ℝ E\nf : ℝ → E\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ι\na b z : ℝ\nu v ua... | [
535,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.subset_zeroLocus_iff_le_vanishingIdeal | [] | [
128,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.copy_eq | [] | [
289,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_cubic_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1218360\n⊢ degree (↑C a * X ^ 3 + ↑C b * X ^ 2 + ↑C c * X + ↑C d) ≤ 3",
"tactic": "simpa only [add_assoc] using\n degree_add_le_of_degree_le (degree_C_mul_X_pow_le 3 a... | [
1213,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nat_le_lift_iff | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\na : Cardinal\n⊢ ↑n ≤ lift a ↔ ↑n ≤ a",
"tactic": "rw [← lift_natCast.{v,u}, lift_le]"
}
] | [
1303,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.mk_apply | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.homEquiv_id | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X✝ : C\nY Y' : D\nX : C\n⊢ ↑(homEquiv adj X (F.obj X)) (𝟙 (F.obj X)) = adj.unit.app X",
"tactic": "simp"
}
] | [
139,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | nonPrincipals_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝ : CommRing R\n⊢ nonPrincipals R = ∅ ↔ IsPrincipalIdealRing R",
"tactic": "simp [Set.eq_empty_iff_forall_not_mem, isPrincipalIdealRing_iff, nonPrincipals_def]"
}
] | [
485,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.lift_fst | [] | [
628,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_exists_left_inv | [] | [
964,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_sup | [
{
"state_after": "u v : PrimeMultiset\nn : ℕ+ := prod u\n⊢ prod (u ⊔ v) = PNat.lcm (prod u) (prod v)",
"state_before": "u v : PrimeMultiset\n⊢ prod (u ⊔ v) = PNat.lcm (prod u) (prod v)",
"tactic": "let n := u.prod"
},
{
"state_after": "u v : PrimeMultiset\nn : ℕ+ := prod u\nm : ℕ+ := prod v\n⊢ p... | [
428,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le | [
{
"state_after": "α✝ β✝ α : Type u\nβ : Type v\nc : Cardinal\nf : α → β\nhf : ∀ (b : β), lift (#↑(f ⁻¹' {b})) ≤ c\nb : β\n⊢ ↑(↑Equiv.ulift.symm ⁻¹' ((fun x => { down := f x.down }) ⁻¹' {{ down := b }})) ≃ ↑(f ⁻¹' {b})",
"state_before": "α✝ β✝ α : Type u\nβ : Type v\nc : Cardinal\nf : α → β\nhf : ∀ (b : β), ... | [
934,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.swap_surjective | [] | [
201,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasStrictFDerivAt.const_rpow | [] | [
498,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.compl_iff | [] | [
100,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_iff_exists_right | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.264410\nP : Type u_3\nP' : Type ?u.264416\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y p₂ : P\n... | [
507,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_Ioo_atTop | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf✝ : α → β\nf : β → ↑(Ioo a b)\n⊢ Tendsto (Subtype.val ∘ f) l (𝓝[Iio b] b) ↔ Tendsto (fun x => ↑(f x)) l (𝓝[Iio b] b)... | [
2560,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2558,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_add_one_iff | [] | [
220,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_nonneg_of_forall | [] | [
1367,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_smul_right_of_pos | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nr : ℝ\nhr : 0 < r\n⊢ arccos (inner x (r • y) / (‖x‖ * ‖r • y‖)) = arccos (inner x y / (‖x‖ * ‖y‖))",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝... | [
158,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.id | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ Nat.pair (unpair n).fst (unpair n).snd = id n",
"tactic": "simp"
}
] | [
103,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mul_norm_le_Lp_mul_Lq | [
{
"state_after": "α : Type u_2\nE✝ : Type ?u.1514701\nF : Type ?u.1514704\n𝕜 : Type ?u.1514707\ninst✝¹¹ : NormedAddCommGroup E✝\ninst✝¹⁰ : NormedSpace ℝ E✝\ninst✝⁹ : CompleteSpace E✝\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E✝\ninst✝⁶ : SMulCommClass ℝ 𝕜 E✝\ninst✝⁵ : NormedAddCommGroup F\... | [
1694,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1652,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_eq | [] | [
714,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Std/Data/Fin/Lemmas.lean | USize.modn_toNat | [] | [
37,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
36,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.cos | [] | [
950,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/Analysis/Convex/Normed.lean | convexOn_univ_dist | [] | [
62,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/Convex/Independent.lean | convexIndependent_set_iff_not_mem_convexHull_diff | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.41306\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns✝ t s : Set E\n⊢ (∀ (t : Set E), t ⊆ s → s ∩ ↑(convexHull 𝕜).toOrderHom t ⊆ t) ↔\n ∀ (x : E), x ∈ s → ¬x ∈ ↑(convexHull 𝕜).toOrderHom (s \\ {x})",
"state_before"... | [
168,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.IsBoundedUnder.bddBelow_range | [] | [
163,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.sections_cons | [] | [
41,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.top_apply | [] | [
379,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Analysis/SpecificLimits/FloorPow.lean | tendsto_div_of_monotone_of_tendsto_div_floor_pow | [
{
"state_after": "u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nc : ℕ → ℝ\ncone : ∀ (k : ℕ), 1 < c k\nclim : Tendsto c atTop (𝓝 1)\nhc : ∀ (k : ℕ), Tendsto (fun n => u ⌊c k ^ n⌋₊ / ↑⌊c k ^ n⌋₊) atTop (𝓝 l)\n⊢ ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Te... | [
244,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.lt_iff | [] | [
308,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_self_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.32722\nR : Type u_2\nR₂ : Type ?u.32728\nK : Type ?u.32731\nM : Type u_3\nM' : Type ?u.32737\nM'' : Type ?u.32740\nV : Type u\nV' : Type ?u.32745\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMono... | [
163,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_nonsing_inv | [
{
"state_after": "case intro\nl : Type ?u.190911\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nh : IsUnit (det A)\nval✝ : Invertible A\n⊢ A ⬝ A⁻¹ = 1",
"state_before": "l : Type ?u.190911\nm : Type u\nn : Type u'\nα : Type v\ninst✝²... | [
305,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_comap_le | [] | [
1658,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1657,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomainInv.isUnit | [] | [
288,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
11
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.size_eq_natSize | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.333835\nn : PosNum\n⊢ ↑(size (bit0 n)) = natSize (bit0 n)",
"tactic": "rw [size, succ_to_nat, natSize, size_eq_natSize n]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.333835\nn : PosNum\n⊢ ↑(size (bit1 n)) = natSize (... | [
578,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nonempty_coe_sort | [] | [
449,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.ediam_image_le_of_subset_of_le | [] | [
174,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
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