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/GroupTheory/Nilpotent.lean | isNilpotent_of_ker_le_center | [
{
"state_after": "G : Type u_2\ninst✝² : Group G\nH✝ : Subgroup G\ninst✝¹ : Normal H✝\nH : Type u_1\ninst✝ : Group H\nf : G →* H\nhf1 : MonoidHom.ker f ≤ center G\nhH : ∃ n, lowerCentralSeries H n = ⊥\n⊢ ∃ n, lowerCentralSeries G n = ⊥",
"state_before": "G : Type u_2\ninst✝² : Group G\nH✝ : Subgroup G\ninst... | [
525,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Order/Disjoint.lean | top_disjoint | [] | [
115,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Logic/Basic.lean | of_not_imp | [] | [
257,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Order/Grade.lean | isMax_grade_iff | [] | [
157,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_mul_le | [] | [
91,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/Algebra/Ring/Divisibility.lean | dvd_mul_sub_mul | [
{
"state_after": "case h.e'_4\nα : Type u_1\nβ : Type ?u.14179\ninst✝ : NonUnitalCommRing α\na✝ b✝ c k a b x y : α\nhab : k ∣ a - b\nhxy : k ∣ x - y\n⊢ a * x - b * y = a * (x - y) + (a - b) * y",
"state_before": "α : Type u_1\nβ : Type ?u.14179\ninst✝ : NonUnitalCommRing α\na✝ b✝ c k a b x y : α\nhab : k ∣ ... | [
171,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.head_cons | [] | [
257,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_one_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.296904\nE : Type u_2\nF : Type u_3\nG : Type ?u.296913\nE' : Type ?u.296916\nF' : Type ?u.296919\nG' : Type ?u.296922\nE'' : Type ?u.296925\nF'' : Type ?u.296928\nG'' : Type ?u.296931\nR : Type ?u.296934\nR' : Type ?u.296937\n𝕜 : Type ?u.296940\n𝕜' : Type ?u.296943\... | [
1332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
1
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Mathlib/Data/Set/Finite.lean | Set.card_insert | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\na : α\ns : Set α\ninst✝ : Fintype ↑s\nh : ¬a ∈ s\nd : Fintype ↑(insert a s)\n⊢ Fintype.card ↑(insert a s) = Fintype.card ↑(insert a s)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\na : α\ns : Set α\ninst✝ : Fintype ↑s\nh ... | [
1210,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
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Mathlib/FieldTheory/Subfield.lean | Subfield.not_mem_of_not_mem_closure | [] | [
706,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Order/Lattice.lean | right_eq_inf | [] | [
449,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.mkRingHom_rel | [
{
"state_after": "no goals",
"state_before": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : Type u₃\ninst✝¹ : Semiring A\ninst✝ : Algebra S A\nr✝ r : R → R → Prop\nx y : R\nw : r x y\n⊢ ↑(mkRingHom r) x = ↑(mkRingHom r) y",
"tactic": "simp [mkRingHom_def, Quot.sound (Rel.of... | [
402,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_div_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.65810\nα : Type u_1\nβ : Type ?u.65816\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\nhc : 0 < c\n⊢ a / b < a / c ↔ c < b",
"tactic": "simp only [div_eq_mul_inv, mul_lt_mul_left ha, inv_lt_inv hb hc]"
}
] | [
374,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Int/GCD.lean | Int.dvd_of_dvd_mul_left_of_gcd_one | [
{
"state_after": "a b c : ℤ\nhabc : a ∣ b * c\nhab : gcd a c = 1\nthis : ↑(gcd a c) = a * gcdA a c + c * gcdB a c\n⊢ a ∣ b",
"state_before": "a b c : ℤ\nhabc : a ∣ b * c\nhab : gcd a c = 1\n⊢ a ∣ b",
"tactic": "have := gcd_eq_gcd_ab a c"
},
{
"state_after": "a b c : ℤ\nhabc : a ∣ b * c\nhab : gc... | [
417,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
src/lean/Init/Data/List/Basic.lean | List.length_reverse | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas : List α\n⊢ length (reverse as) = length as",
"tactic": "induction as with\n| nil => rfl\n| cons a as ih => simp [ih]"
},
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u\nβ : Type v\nγ : T... | [
803,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
800,
9
] |
Mathlib/Algebra/Order/Field/Basic.lean | mul_inv_le_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.33547\nα : Type u_1\nβ : Type ?u.33553\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : 0 < b\n⊢ a * b⁻¹ ≤ c ↔ a ≤ c * b",
"tactic": "rw [mul_comm, inv_mul_le_iff' h]"
}
] | [
189,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_prod | [] | [
1115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.lift_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\nB : Type ?u.109263\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq : Basis A c₁ c₂\nr : R\nx : ℍ[R,c₁,c₂]\n⊢ lift q (r • x) = r • lift q x",
"tactic": "simp [lift, mu... | [
145,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Algebra/Hom/Units.lean | eq_on_inv | [] | [
64,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.coe_trans | [] | [
275,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
9
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.congr' | [] | [
476,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_sdiff | [
{
"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.111150\ns₂✝ : Finset ι₂\ninst✝ : DecidableEq ι\ns₂ : Finset ι\nh : s₂ ⊆ s\nw : ι → k\np : ι → P... | [
213,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.neg_const_mul_atBot | [] | [
1229,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.Subtype.coe_bot | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | SubmonoidClass.coe_pow | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.countable | [
{
"state_after": "case inl\nι : Type ?u.2072778\nα : Type u_1\nβ : Type ?u.2072784\nf g : Perm α\nt : Set α\na b x y : α\nhs : IsCycleOn f ∅\n⊢ Set.Countable ∅\n\ncase inr.intro\nι : Type ?u.2072778\nα : Type u_1\nβ : Type ?u.2072784\nf g : Perm α\ns t : Set α\na✝ b x y : α\nhs : IsCycleOn f s\na : α\nha : a ∈ ... | [
947,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
11
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_mk | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_tsub_tsub_cancel_left | [] | [
303,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mapEquiv_symm | [] | [
834,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Analysis/Convex/Extrema.lean | IsMaxOn.of_isLocalMax_of_convex_univ | [] | [
89,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.exists_range_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.12684\nδ : Type ?u.12687\ninst✝ : MeasurableSpace α\nf : α →ₛ β\np : β → Prop\n⊢ (∃ y, y ∈ SimpleFunc.range f ∧ p y) ↔ ∃ x, p (↑f x)",
"tactic": "simpa only [mem_range, exists_prop] using Set.exists_range_iff"
}
] | [
130,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Real/Sqrt.lean | ContinuousOn.sqrt | [] | [
499,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.not_mem_top | [] | [
572,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_singleton_iff_nonempty_unique_mem | [] | [
1368,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Data/MvPolynomial/Funext.lean | MvPolynomial.funext | [
{
"state_after": "R : Type u_2\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : Infinite R\nσ : Type u_1\np q : MvPolynomial σ R\nh : ∀ (x : σ → R), ↑(eval x) p = ↑(eval x) q\n⊢ ∀ (p : MvPolynomial σ R), (∀ (x : σ → R), ↑(eval x) p = 0) → p = 0",
"state_before": "R : Type u_2\ninst✝² : CommRing R\ninst✝¹ ... | [
62,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/PathConnected.lean | pathComponent_congr | [
{
"state_after": "case h\nX : Type u_1\nY : Type ?u.624861\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z✝ : X\nι : Type ?u.624876\nF : Set X\nh : x ∈ pathComponent y\nz : X\n⊢ z ∈ pathComponent x ↔ z ∈ pathComponent y",
"state_before": "X : Type u_1\nY : Type ?u.624861\ninst✝¹ : Topologica... | [
928,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/Topology/Homotopy/HSpaces.lean | unitInterval.continuous_qRight | [
{
"state_after": "no goals",
"state_before": "⊢ Continuous fun p => 2 * ↑p.fst",
"tactic": "continuity"
},
{
"state_after": "no goals",
"state_before": "⊢ Continuous fun p => 1 + ↑p.snd",
"tactic": "continuity"
}
] | [
189,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/List/Basic.lean | List.foldr_map' | [
{
"state_after": "case nil\nι : Type ?u.234464\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα β : Type u\ng : α → β\nf : α → α → α\nf' : β → β → β\nh : ∀ (x y : α), f' (g x) (g y) = g (f x y)\na : α\n⊢ foldr f' (g a) (map g []) = g (foldr f a [])\n\ncase cons\nι : Type ?u.234464\nα✝ : Typ... | [
2485,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2480,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.id_whiskerLeft_symm | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf g : a ⟶ b\nη : f ⟶ g\n⊢ η = (λ_ f).inv ≫ 𝟙 a ◁ η ≫ (λ_ g).hom",
"tactic": "simp"
}
] | [
400,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Analysis/Filter.lean | CFilter.mem_toFilter_sets | [] | [
95,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Int/LeastGreatest.lean | Int.coe_greatestOfBdd_eq | [
{
"state_after": "case mk.intro\nP : ℤ → Prop\ninst✝ : DecidablePred P\nb b' : ℤ\nHb : ∀ (z : ℤ), P z → z ≤ b\nHb' : ∀ (z : ℤ), P z → z ≤ b'\nHinh : ∃ z, P z\nn : ℤ\nhn : P n\nh2n : ∀ (z : ℤ), P z → z ≤ n\n⊢ ↑{ val := n, property := (_ : P n ∧ ∀ (z : ℤ), P z → z ≤ n) } = ↑(greatestOfBdd b' Hb' Hinh)",
"stat... | [
114,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.inv_mk | [] | [
727,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.monotone_comap | [] | [
499,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.toRingHom_eq_coe | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.coe_coe | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : AddGroupWithOne R\nf : ArithmeticFunction ℕ\nx✝ : ℕ\n⊢ ↑↑↑f x✝ = ↑↑f x✝",
"state_before": "R : Type u_1\ninst✝ : AddGroupWithOne R\nf : ArithmeticFunction ℕ\n⊢ ↑↑f = ↑f",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h\n... | [
191,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.isGreatest_gfp | [] | [
144,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.linMulLin_comp | [] | [
600,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_eq_left | [
{
"state_after": "no goals",
"state_before": "a b : Cardinal\nha : ℵ₀ ≤ a\nhb : b ≤ a\n⊢ a + b = a",
"tactic": "rw [add_eq_max ha, max_eq_left hb]"
}
] | [
780,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Data/Fintype/Sum.lean | Fintype.card_sum | [] | [
41,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_isTorsionBySet | [] | [
358,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | right_le_lineMap_iff_le | [] | [
164,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Std/Data/Int/DivMod.lean | Int.sign_eq_div_abs | [
{
"state_after": "no goals",
"state_before": "a : Int\naz : a = 0\n⊢ sign a = div a ↑(natAbs a)",
"tactic": "simp [az]"
}
] | [
837,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
834,
11
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.monic_toSubring | [
{
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389,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
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Mathlib/Data/Set/Function.lean | StrictAntiOn.mono | [] | [
312,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
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Mathlib/Topology/List.lean | List.continuous_insertNth | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.54167\ninst... | [
149,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.irreducible_of_coprime' | [
{
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374,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/Topology/Sober.lean | IsGenericPoint.isClosed | [] | [
75,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
11
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_def | [
{
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}
] | [
665,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
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Mathlib/Algebra/Jordan/Basic.lean | commute_lmul_rmul | [] | [
143,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.transReflReparamAux_one | [
{
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"tactic": "simp [transReflReparamAu... | [
161,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.ofInt_re | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.pullback_self | [] | [
291,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_commonNeighbors_le_degree_right | [
{
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... | [
1605,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1603,
1
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Std/Data/Int/Lemmas.lean | Int.natAbs_pos | [
{
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}
] | [
151,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
151,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.inr_apply | [] | [
964,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_right | [] | [
854,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
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Mathlib/Algebra/GeomSum.lean | geom_sum₂_Ico | [] | [
352,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.mul | [
{
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1067,
88
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1061,
11
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Mathlib/LinearAlgebra/Basis.lean | Basis.apply_eq_iff | [] | [
310,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/Logic/Equiv/Fintype.lean | Equiv.extendSubtype_not_mem | [
{
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143,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.proj_continuous | [] | [
64,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.nfpFamily_lt_ord_of_isRegular | [
{
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}
] | [
1134,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
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Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | one_lt_mul_iff | [
{
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"tactic": "simp only [one_lt_iff_ne_one, Ne.def, mul_eq_one_iff, not_and_or]"
}
] | [
258,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid.left | [] | [
1104,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
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Mathlib/Combinatorics/Young/SemistandardTableau.lean | Ssyt.zeros | [] | [
125,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Algebra/Lie/OfAssociative.lean | LieModule.toEndomorphism_module_end | [
{
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244,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eqOn_right_half_plane_of_superexponential_decay | [
{
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889,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bit_val | [
{
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"state_before": "b : Bool\nn : ℕ\n⊢ bit b n = 2 * n + bif b then 1 else 0",
"tactic": "cases b"
},
{
"state_after": "case true\nn : ℕ\n⊢ bit t... | [
167,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensorHom_inv_id | [
{
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"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V✝ W✝ X✝ Y✝ Z✝ V W X Y Z : C\nf : V ≅ W\ng : X ⟶ Y\nh : Y ⟶ Z\n⊢ (g ⊗ f.hom) ≫ (h ⊗ f.inv) = (g ⊗ 𝟙 V) ≫ (h ⊗ 𝟙 V)",
"tactic": "rw [... | [
368,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Int/NatPrime.lean | Int.Prime.dvd_natAbs_of_coe_dvd_sq | [
{
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"state_before": "p : ℕ\nhp : Nat.Prime p\nk : ℤ\nh : ↑p ∣ k ^ 2\n⊢ p ∣ natAbs k",
"tactic": "apply @Nat.Prime.dvd_of_dvd_pow _ _ 2 hp"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Nat.Prime... | [
42,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_insert | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.3612\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\ninst✝ : DecidableEq β\nb : β\nh : b ∈ s\n⊢ lcm (insert b s) f = GCDMonoid.lcm (f b) (lcm s f)\n\ncase neg\nα : Type u_2\nβ : Type u_1\nγ :... | [
85,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.v_eq_succ_vp | [
{
"state_after": "no goals",
"state_before": "u : XgcdType\n⊢ v u = succ₂ (vp u)",
"tactic": "ext <;> dsimp [v, vp, w, z, a, b, succ₂] <;> (repeat' rw [Nat.succ_eq_add_one]; ring_nf)"
},
{
"state_after": "no goals",
"state_before": "case h₂\nu : XgcdType\n⊢ u.y * succ u.ap + succ u.zp * succ... | [
140,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Set/Prod.lean | Set.univ_pi_singleton | [
{
"state_after": "no goals",
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"tactic": "simp [funext_iff]"
}
] | [
741,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.le_opNorm | [
{
"state_after": "case intro.intro\nV : Type ?u.224218\nV₁ : Type u_2\nV₂ : Type u_1\nV₃ : Type ?u.224227\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf g : NormedAddGroupHom V₁ V₂\nx : V₁\nC : ℝ\n_Cpos : 0 < C\nhC... | [
250,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.Memℒp.snorm_indicator_norm_ge_le | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nι : Type ?u.99807\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : α → β\nhf : Memℒp f p\nhmeas : StronglyMeasurable f\nε : ℝ\nhε : 0 < ε\nhp_ne_zero : p = 0\n⊢ ∃ M, snorm (Set.indicator {x | M ≤ ↑‖f x‖₊} f) p μ ≤ ENNReal.... | [
296,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Filter.Tendsto.isCoboundedUnder_le | [] | [
113,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_comp_rpow_iff' | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\np : ℝ\nhp : p ≠ 0\n⊢ IntegrableOn (fun x => x ^ (p - 1) • f (x ^ p)) (Ioi 0) ↔ IntegrableOn f (Ioi 0)",
"tactic": "simpa only [← integrableOn_Ioi_comp_rpow_iff f hp, mul_smul] u... | [
935,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_sup | [] | [
457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.uniformContinuous_quotient_mk | [] | [
295,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.SetIndependent.pairwiseDisjoint | [] | [
208,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Std/Data/List/Lemmas.lean | List.removeNth_eq_nth_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ removeNth l 0 = modifyNthTail tail 0 l",
"tactic": "cases l <;> rfl"
}
] | [
725,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
722,
1
] |
Mathlib/Order/Bounds/OrderIso.lean | OrderIso.isLUB_preimage' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α ≃o β\ns : Set β\nx : β\n⊢ IsLUB (↑f ⁻¹' s) (↑(symm f) x) ↔ IsLUB s x",
"tactic": "rw [isLUB_preimage, f.apply_symm_apply]"
}
] | [
60,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.inr_inj | [] | [
158,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_injective | [] | [
1002,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMonoOn.eq_iff_eq | [
{
"state_after": "ι : Type ?u.27119\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.27128\nπ : ι → Type ?u.27133\nr : α → α → Prop\ninst✝¹ : LinearOrder α\ninst✝ : Preorder β\nf : α → β\ns : Set α\nhf : StrictMonoOn f s\na : α\nha hb : a ∈ s\n⊢ f a = f a",
"state_before": "ι : Type ?u.27119\nα : Type u\nβ ... | [
788,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isOrthoᵢ_def | [] | [
92,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
src/lean/Init/Core.lean | Quot.liftBeta | [] | [
1216,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1211,
11
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_isNormal | [
{
"state_after": "no goals",
"state_before": "a : Ordinal\nh : 1 < a\na0 : 0 < a\nb : Ordinal\n⊢ (fun x x_1 => x ^ x_1) a b < (fun x x_1 => x ^ x_1) a (succ b)",
"tactic": "simpa only [mul_one, opow_succ] using (mul_lt_mul_iff_left (opow_pos b a0)).2 h"
}
] | [
112,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/Basic.lean | eq_of_le_of_forall_le_of_dense | [] | [
1315,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1313,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.eq_zero_iff | [] | [
204,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
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