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/LinearAlgebra/Basis.lean | Basis.maximal | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.778808\nR : Type u_1\nR₂ : Type ?u.778814\nK : Type ?u.778817\nM : Type u_3\nM' : Type ?u.778823\nM'' : Type ?u.778826\nV : Type u\nV' : Type ?u.778831\nv : ι → M\ninst✝⁹ : Ring R\ninst✝⁸ : CommRing R₂\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : AddCommGroup M'\ninst✝⁵ : AddC... | [
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1092,
1
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Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_of_subsingleton | [] | [
181,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/RingTheory/IntegralDomain.lean | Polynomial.div_eq_quo_add_rem_div | [
{
"state_after": "case refine'_1\nR : Type u_1\nG : Type ?u.275691\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : Group G\nK : Type\ninst✝² : Field K\ninst✝¹ : Algebra R[X] K\ninst✝ : IsFractionRing R[X] K\nf g : R[X]\nhg : Monic g\n⊢ degree (f %ₘ g) < degree g\n\ncase refine'_2\nR : Type u_1\nG : Type ?u.... | [
188,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/Topology/MetricSpace/Basic.lean | dist_dist_dist_le | [] | [
1784,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1782,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_add_subset | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.157002\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np✝ q✝ : MvPolynomial σ R\ninst✝ : DecidableEq σ\np q : MvPolynomial σ R\nx : σ\nhx : x ∈ vars (p + q)\n⊢ x ∈ vars p ∪ vars q",
"state_before": "R : Type u\nS : Type v\nσ : ... | [
330,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Std/Data/List/Lemmas.lean | List.prefix_append_right_inj | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ l r : List α✝\n⊢ l ++ l₁ ++ r = l ++ l₂ ↔ l₁ ++ r = l₂",
"tactic": "rw [append_assoc, append_right_inj]"
}
] | [
1710,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1709,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.sum_totient' | [
{
"state_after": "case h.e'_2\nn : ℕ\n⊢ ∑ m in filter (fun x => x ∣ n) (range (succ n)), φ m = Finset.sum (divisors n) φ",
"state_before": "n : ℕ\n⊢ ∑ m in filter (fun x => x ∣ n) (range (succ n)), φ m = n",
"tactic": "convert sum_totient _ using 1"
},
{
"state_after": "case h.e'_2\nn : ℕ\n⊢ (∑ ... | [
188,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
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 → i ≠ a → i ≠ b → IsPrime (f i)\nI : Ideal R\nthis : (↑I ⊆ ⋃ (i : ι) (_ : i ∈ ↑s), ↑(f i)) → ∃ i, i ∈ s ∧ I ≤ f i\naux : (↑I ⊆... | [
1255,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/CategoryTheory/Sites/CompatibleSheafification.lean | CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app | [
{
"state_after": "C : Type u\ninst✝⁸ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁷ : Category D\nE : Type w₂\ninst✝⁶ : Category E\nF : D ⥤ E\ninst✝⁵ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁴ : ∀ (α β : Type (max v u)) (fst snd : β → α),... | [
118,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.Subsingleton.aestronglyMeasurable | [] | [
1165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.mapAlgHom_id | [] | [
1404,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.not_all_isQF | [
{
"state_after": "case of_isAtomic\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.113613\nP : Type ?u.113616\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.113644\nn l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv :... | [
742,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.pow_comp | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_add | [] | [
478,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.atTop_neBot | [] | [
153,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/ModelTheory/Substructures.lean | Set.Countable.substructure_closure | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.35964\nP : Type ?u.35967\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nS : Substructure L M\ns : Set M\ninst✝ : Countable ((l : ℕ) × Functions L l)\nh : Set.Countable s\nthis : Countable ↑s\n⊢ Countable { x // x ∈ LowerAdjoint.to... | [
343,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.le_def | [] | [
124,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_modEq_a_sub_one | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ yn a1 0 ≡ 0 [MOD a - 1]",
"tactic": "simp [Nat.ModEq.refl]"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ yn a1 1 ≡ 1 [MOD a - 1]",
"tactic": "simp [Nat.ModEq.refl]"
},
{
"state_after": "a ... | [
553,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\np q : R[X]\nn : ℕ\n⊢ degree (X ^ n) = ↑n",
"tactic": "rw [X_pow_eq_monomial, degree_monomial _ (one_ne_zero' R)]"
}
] | [
1258,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.alternatingFaceMapComplex_obj_X | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_pNat | [] | [
1891,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1890,
1
] |
Mathlib/Data/Int/Basic.lean | Int.succ_neg_succ | [
{
"state_after": "no goals",
"state_before": "a : ℤ\n⊢ succ (-succ a) = -a",
"tactic": "rw [neg_succ, succ_pred]"
}
] | [
161,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mul_imK | [] | [
340,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
9
] |
Mathlib/Computability/Partrec.lean | Computable.comp₂ | [] | [
536,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.IsComplete.models_not_iff | [
{
"state_after": "case inl\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nh : IsComplete T\nφ : Sentence L\nhφ : T ⊨ᵇ φ\n⊢ T ⊨ᵇ Formula.not φ ↔ ¬T ⊨ᵇ φ\n\ncase inr\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nh : IsComplete T\nφ : Sentence L\nhφn : T ⊨ᵇ Formula.not φ\n⊢ T ⊨ᵇ Formula.not φ ↔ ¬T ⊨ᵇ φ",
"s... | [
376,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.blsub_lt_ord_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.159211\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nc : Cardinal\nhc : IsRegular c\nho : card o < c\n⊢ card o < Ordinal.cof (ord c)",
"tactic": "rwa [hc.cof_eq]"
}
] | [
1089,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.121824\ninst✝ : Fintype ι\na b : ℝ\n⊢ ↑↑volume (Ioc a b) = ofReal (b - a)",
"tactic": "simp [volume_val]"
}
] | [
95,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.one_le_aleph0 | [] | [
1418,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_neg | [] | [
209,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.zero_left | [] | [
1208,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.generateFrom_mono | [] | [
433,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_of_mem_powerset | [] | [
2137,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2137,
1
] |
Mathlib/Topology/Order/Basic.lean | Monotone.map_sInf_of_continuousAt | [] | [
2688,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2686,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝³ : Preorder α\ninst✝² : Preorder β\ns t : Set α\na✝ b✝ : α\ninst✝¹ : SemilatticeInf γ\ninst✝ : DenselyOrdered γ\na b : γ\nhab : a < b\n⊢ IsLUB (Ioo a b) b",
"tactic": "simpa only [dual_Ioo] using isGLB_Io... | [
768,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.exists_left_inv | [
{
"state_after": "case intro.mk\nα : Type u\nM : Type u_1\nN : Type ?u.57084\ninst✝ : Monoid M\na b : M\nval_inv✝ : a * b = 1\nhba : b * a = 1\n⊢ ∃ b_1, b_1 * ↑{ val := a, inv := b, val_inv := val_inv✝, inv_val := hba } = 1",
"state_before": "α : Type u\nM : Type u_1\nN : Type ?u.57084\ninst✝ : Monoid M\na ... | [
644,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.card_pow_eq_one_le | [
{
"state_after": "α : Type u\na : α\ninst✝³ : Group α\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\ninst✝ : IsCyclic α\nn : ℕ\nhn0 : 0 < n\ng : α\nhg : ∀ (x : α), x ∈ zpowers g\nx : α\nhx : x ∈ filter (fun a => a ^ n = 1) univ\nm : ℕ\nhm : g ^ m = x\n⊢ (fun x x_1 => x ^ x_1) (g ^ (Fintype.card α / Nat.gcd n (Fin... | [
276,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.tendsto_leftLim | [] | [
338,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul | [
{
"state_after": "R✝ : Type ?u.23931\nM✝ : Type ?u.23934\ninst✝⁵ : Semiring R✝\ninst✝⁴ : AddCommMonoid M✝\ninst✝³ : Module R✝ M✝\nR : Type u_1\ninst✝² : CommRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nN : Submodule R M\nhn : ∃ S, Set.Finite S ∧ span R S = N\nhin : N ≤ I • N\n... | [
136,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithTop.pred_coe | [] | [
1105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.abs_cos_add_sin_mul_I | [
{
"state_after": "x : ℝ\nthis : Real.sin x ^ 2 + Real.cos x ^ 2 = 1\n⊢ ↑abs (cos ↑x + sin ↑x * I) = 1",
"state_before": "x : ℝ\n⊢ ↑abs (cos ↑x + sin ↑x * I) = 1",
"tactic": "have := Real.sin_sq_add_cos_sq x"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nthis : Real.sin x ^ 2 + Real... | [
2025,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2023,
1
] |
Mathlib/Order/Minimal.lean | maximals_subset | [] | [
45,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.isMax_iterate_succ_of_eq_of_lt | [
{
"state_after": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : SuccOrder α\na b : α\nn m : ℕ\nh_eq : (succ^[n]) a = (succ^[m]) a\nh_lt : n < m\n⊢ succ ((succ^[n]) a) ≤ (succ^[m]) a",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : SuccOrder α\na b : α\nn m : ℕ\nh_eq : (succ^[n]) a = (succ^[m]) a\n... | [
292,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.subsingleton_sphere | [] | [
2912,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2911,
1
] |
Mathlib/Data/Sigma/Basic.lean | Function.Surjective.sigma_map | [
{
"state_after": "α : Type ?u.7362\nα₁ : Type u_1\nα₂ : Type u_2\nβ : α → Type ?u.7373\nβ₁ : α₁ → Type u_3\nβ₂ : α₂ → Type u_4\nf₁ : α₁ → α₂\nf₂ : (a : α₁) → β₁ a → β₂ (f₁ a)\nh₁ : Surjective f₁\nh₂ : ∀ (a : α₁), Surjective (f₂ a)\n⊢ ∀ (x : α₁) (b : β₂ (f₁ x)), ∃ a, Sigma.map f₁ f₂ a = { fst := f₁ x, snd := b }... | [
138,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.is_norm | [] | [
819,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
11
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Icc ↑a ↑b = Icc a b",
"tactic": "simp [← Ici_inter_Iic]"
}
] | [
60,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_of_mul_apply_of_le | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nσ : Type u_2\nS : Type ?u.381766\nR : Type u_1\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : Semiring R\ninst✝⁶ : SetLike σ R\ninst✝⁵ : AddSubmonoidClass σ R\nA : ι → σ\ninst✝⁴ : CanonicallyOrderedAddMonoid ι\ninst✝³ : SetLike.GradedMonoid A\ninst✝² : Sub ι\ni... | [
265,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Group.lean | le_ciInf_mul | [] | [
43,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_singleton | [] | [
185,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsWf.min_mem | [] | [
623,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conjLie_apply | [] | [
956,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.leftUnitor_comp | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\n⊢ (λ_ (f ≫ g)).hom = (α_ (𝟙 a) f g).inv ≫ (λ_ f).hom ▷ g",
"tactic": "simp"
}
] | [
465,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_iff_ofNNReal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.702248\nγ : Type ?u.702251\nδ : Type ?u.702254\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ≥0\n⊢ (HasFiniteIntegral fun x => ↑(f x)) ↔ (∫⁻ (a... | [
137,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/LinearAlgebra/Vandermonde.lean | Matrix.det_vandermonde_ne_zero_iff | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nv : Fin n → R\n⊢ det (vandermonde v) ≠ 0 ↔ ∀ ⦃a₁ a₂ : Fin n⦄, v a₁ = v a₂ → a₁ = a₂",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nv : Fin n → R\n⊢ det (vandermonde v) ≠ 0 ↔ Function.Injective v... | [
157,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.sigmaLcurry_apply | [] | [
264,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.card' | [] | [
164,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Order/BoundedOrder.lean | Subtype.mk_bot | [] | [
763,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.coe_mem | [] | [
177,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/List/Count.lean | List.count_tail | [
{
"state_after": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\nhead : α\ntail : List α\na : α\nh : 0 < length (head :: tail)\n⊢ count a (List.tail (head :: tail)) =\n (count a tail + if a = head then 1 else 0) - if a = get (head :: tail) { val := 0, isLt := h } then 1 else 0",
"state_before": "α : Ty... | [
206,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | QuasiErgodic.ae_empty_or_univ' | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\nhf : QuasiErgodic f\nhs : MeasurableSet s\nhs' : f ⁻¹' s =ᶠ[ae μ] s\nt : Set α\nh₀ : MeasurableSet t\nh₁ : t =ᶠ[ae μ] s\nh₂ : f ⁻¹' t = t\n⊢ s =ᶠ[ae μ] ∅ ∨ s =ᶠ[ae μ] univ",
"sta... | [
126,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.atBot_Iic_eq | [] | [
1592,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1591,
1
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_comp_inv_hom_comp | [] | [
183,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.dropWhile | [
{
"state_after": "l m r : List Char\np : Char → Bool\n⊢ ValidFor (l ++ List.takeWhile p m) (List.dropWhile p m) r\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len l + utf8Len (List.takeWhile p m) },\n stopPos := { byteIdx := utf8Len l + utf8Len m } }",
"state_before": "l m r : Li... | [
949,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
944,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | WellFounded.rank_strictMono | [] | [
2576,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2575,
1
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.cancel_epi_id | [
{
"state_after": "case h.e'_1.h.e'_3.h\nC : Type u\ninst✝¹ : Category C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : Epi f\nh : Y ⟶ Y\n⊢ f = f ≫ 𝟙 Y",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : Epi f\nh : Y ⟶ Y\n⊢ f ≫ h = f ↔ h = 𝟙 Y",
"tactic": "convert cancel_epi f"
},
{
... | [
297,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.extract | [
{
"state_after": "l m r ml mm mr : List Char\nb e : Pos\n⊢ ∃ l' r',\n ValidFor l' mm r'\n (if utf8Len ml + utf8Len mm ≤ utf8Len ml then { str := \"\", startPos := 0, stopPos := 0 }\n else\n { str := { data := l ++ (ml ++ (mm ++ (mr ++ r))) },\n startPos :=\n Pos.min { byt... | [
918,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
907,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_zero | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeries_def | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit0_ne | [] | [
140,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_sdiff | [] | [
937,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Algebra/Homology/HomotopyCategory.lean | CategoryTheory.NatTrans.mapHomotopyCategory_comp | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝⁶ : Category V\ninst✝⁵ : Preadditive V\nc✝ : ComplexShape ι\nW : Type u_3\ninst✝⁴ : Category W\ninst✝³ : Preadditive W\nc : ComplexShape ι\nF G H : V ⥤ W\ninst✝² : Functor.Additive F\ninst✝¹ : Functor.Additive G\ninst✝ : Functor.Ad... | [
224,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.comp_continuousOn_iff | [] | [
524,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_lift_same_le_lift | [] | [
158,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_subset_iff | [
{
"state_after": "F : Type ?u.837747\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.837756\ninst✝² : DecidableEq β\ninst✝¹ : Group α\ninst✝ : MulAction α β\ns t : Finset β\na : α\nb : β\n⊢ ↑(a • s) ⊆ ↑t ↔ ↑s ⊆ ↑(a⁻¹ • t)",
"state_before": "F : Type ?u.837747\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.837756\ninst✝²... | [
1978,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1975,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_negOfNat | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ natAbs (negOfNat n) = n",
"tactic": "cases n <;> rfl"
}
] | [
169,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
168,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_mem_nhds | [] | [
1017,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.drop_succ | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_cancel_left | [] | [
364,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ cosh 0 = 1",
"tactic": "simp [cosh]"
}
] | [
1365,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.integrable_comp_smul_iff | [
{
"state_after": "F : Type u_2\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : IsAddHaarMeasure μ\nf : E → F\nR : ℝ\nhR : R ≠ 0\n⊢ ∀ {g : E → F}, Integ... | [
152,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_eq_zero | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ arccos x = 0 ↔ 1 ≤ x",
"tactic": "simp [arccos, sub_eq_zero]"
}
] | [
395,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.horizontal_strip | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b C : ℝ\nf g : ℂ → E\nz : ℂ\nhfd : DiffContOnCl ℂ f (im ⁻¹' Ioo a b)\nhB :\n ∃ c,\n c < π / (b - a) ∧\n ∃ B, f =O[comap (Abs.abs ∘ re) atTop ⊓ 𝓟 (im ⁻¹' Ioo a b)] fun z => expR (B * expR (c * Abs.abs z.re))\nhle_... | [
231,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_toNonUnitalAlgHom | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp₂_eq_mk | [
{
"state_after": "α : Type u_4\nβ : Type u_2\nγ : Type u_1\nδ : Type u_3\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ng : β → γ → δ\nhg : Continuous (uncurry g)\nf₁ : α →ₘ[μ] β\nf₂ : α →ₘ[μ] γ\n⊢ mk (uncurry g ∘ fun x => (↑f₁... | [
318,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.sMod_mod | [
{
"state_after": "no goals",
"state_before": "p i : ℕ\n⊢ sMod p i % (2 ^ p - 1) = sMod p i",
"tactic": "cases i <;> simp [sMod]"
}
] | [
114,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullback.congrHom_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nW X✝ Y✝ Z✝ X Y Z : C\nf₁ f₂ : X ⟶ Z\ng₁ g₂ : Y ⟶ Z\nh₁ : f₁ = f₂\nh₂ : g₁ = g₂\ninst✝¹ : HasPullback f₁ g₁\ninst✝ : HasPullback f₂ g₂\n⊢ f₂ ≫ 𝟙 Z = 𝟙 X ≫ f₁",
"tactic": "simp [h₁]"
},
{... | [
1377,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.map_valEmbedding_Ici | [
{
"state_after": "case a\nn : ℕ\na b : Fin n\nx : ℕ\n⊢ x ∈ map valEmbedding (Ici a) ↔ x ∈ Icc (↑a) (n - 1)",
"state_before": "n : ℕ\na b : Fin n\n⊢ map valEmbedding (Ici a) = Icc (↑a) (n - 1)",
"tactic": "ext x"
},
{
"state_after": "case a\nn : ℕ\na b : Fin n\nx : ℕ\n⊢ (∃ a_1, a ≤ a_1 ∧ ↑valEmbe... | [
149,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.map_id | [] | [
220,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_insert_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.126146\nγ : Type ?u.126149\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\n⊢ _root_.Disjoint (insert a t) s ↔ ¬a ∈ s ∧ _root_.Disjoint s t",
"tactic": "rw [disjoint_insert_left, _root_.disjoint_comm]"
}
] | [
1278,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1277,
1
] |
Mathlib/Topology/PathConnected.lean | IsPathConnected.exists_path_through_family' | [
{
"state_after": "case intro\nX✝ : Type ?u.681883\nY : Type ?u.681886\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.681901\nF : Set X✝\nX : Type u_1\ninst✝ : TopologicalSpace X\nn : ℕ\ns : Set X\nh : IsPathConnected s\np : Fin (n + 1) → X\nhp : ∀ (i : Fin (n + 1)), p i ∈ s\... | [
1080,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_pair | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.267878\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ : P\n⊢ ∃ p₀ v, ∀ (p : P), p ∈ {p₁, p₂} → ∃ r, p = r • v +ᵥ p₀",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι :... | [
439,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Order/Max.lean | IsMin.not_lt | [] | [
313,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/Finset/Functor.lean | Finset.pure_def | [] | [
62,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit1_le | [] | [
692,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
11
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.exp_eq_exp_iff_exp_sub_eq_one | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ exp x = exp y ↔ exp (x - y) = 1",
"tactic": "rw [exp_sub, div_eq_one_iff_eq (exp_ne_zero _)]"
}
] | [
156,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | inv_smul_eq_iff | [] | [
113,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/List/Zip.lean | List.nthLe_zipWith | [] | [
414,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.coeff_sub | [] | [
83,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nB : Type ?u.32898\ninst✝² : LinearOrderedAddCommGroup 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\np x : 𝕜\n⊢ ↑x = 0 ↔ ∃ n, n • p = x",
"tactic": "simp [AddSubgroup.mem_zmultiples_iff]"
}
] | [
175,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_left_inj | [
{
"state_after": "no goals",
"state_before": "a b d : Int\nhda : d ∣ a\nhdb : d ∣ b\nh : a / d = b / d\n⊢ a = b",
"tactic": "rw [← Int.mul_ediv_cancel' hda, ← Int.mul_ediv_cancel' hdb, h]"
}
] | [
822,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
819,
19
] |
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