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/Topology/Order/Basic.lean | Ioc_mem_nhdsWithin_Iio | [] | [
479,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Topology/Partial.lean | ptendsto'_nhds | [] | [
47,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Data/Finset/Basic.lean | Finset.coe_toList | [] | [
3383,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3382,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_restrictVarLeft | [
{
"state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.12423\nP : Type ?u.12426\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\ninst✝ : DecidableEq α\nγ : Type u_1\nt : Term L (α ⊕ γ)\ns : Set α\nh✝ : ↑(varFinsetLeft t) ⊆ s\nv : α → M\... | [
158,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Std/Data/Int/Lemmas.lean | Int.pred_toNat | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ toNat (↑(n + 1) - 1) = toNat ↑(n + 1) - 1",
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}
] | [
1396,
18
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1393,
9
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | IsUnit.aestronglyMeasurable_const_smul_iff | [] | [
1766,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
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Mathlib/Algebra/Lie/Abelian.lean | LieModule.mem_ker | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\n... | [
118,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/Order/Antisymmetrization.lean | Antisymmetrization.ind | [] | [
117,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
11
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.sInf_toSubsemiring | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS : Set (Subalgebra R A)\n⊢ ↑(sInf S).toSubsemiring = ↑(sInf (Subalgebra.toSubsemiring '' S))",
"tactic": "simp"... | [
872,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_gt_three | [
{
"state_after": "no goals",
"state_before": "⊢ 3 < π",
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}
] | [
170,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Logic/Lemmas.lean | ite_ite_distrib_right | [] | [
71,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.formPerm_eq_self_of_not_mem | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : DecidableEq α\ns s' : Cycle α\nx : α\na✝ : List α\nh : Nodup (Quot.mk Setoid.r a✝)\nhx : ¬x ∈ Quot.mk Setoid.r a✝\n⊢ ↑(formPerm (Quot.mk Setoid.r a✝) h) x = x",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ s' s : Cycle α\nh : Nodup s\nx : α\nhx : ¬... | [
180,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_map | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.414392\nβ✝ : Type ?u.414395\nγ : Type ?u.414398\ninst✝¹ : DecidableEq α✝\nα : Type u_1\nβ : Type u_2\nf : α → β\ns : Multiset α\ninst✝ : DecidableEq β\nb : β\n⊢ count b (map f s) = ↑card (filter (fun a => b = f a) s)",
"tactic": "simp [Bool.beq_... | [
2535,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2533,
1
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.preimage | [] | [
1563,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
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Mathlib/CategoryTheory/Linear/LinearFunctor.lean | CategoryTheory.Functor.map_smul | [] | [
52,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_prod_of_monic | [] | [
276,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_sSup_of_directedOn | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S✝\ninst✝ : NonAssocSemiring T\nS : Set (Subsemiring R)\nSne : Set.Nonempty S\nhS : DirectedOn (fun x x_1 => x ≤ x_1) S\nx : R\n⊢ x ∈ ↑(sSup S) ↔ x ∈ ⋃ (... | [
1115,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1113,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_add | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.31525\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\n⊢ (Finset.sup (support (p + q)) fun s => ↑toMultiset s) ≤\n (Finset.sup (support p) fun s => ↑toMulti... | [
148,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.inv_apply_apply | [] | [
204,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.symm_symm | [] | [
758,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_indicator | [
{
"state_after": "α : Type u_1\nβ : Type ?u.948903\nγ : Type ?u.948906\nδ : Type ?u.948909\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\n⊢ (⨆ (x : { i // ↑i ≤ fun a => indicator s f a }), SimpleFunc.lintegral (↑x) μ) =\n ⨆ (x : { i // ↑i ≤ fun a => f a }), SimpleFunc... | [
781,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
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] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.exists_measurable_superset_eq_trim | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nm✝ m : OuterMeasure α\ns : Set α\n⊢ ∃ t, s ⊆ t ∧ MeasurableSet t ∧ ↑m t = ⨅ (t : Set α) (_ : s ⊆ t) (_ : MeasurableSet t), ↑m t",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nm✝ m : OuterMeasure α\ns : Set α\n⊢ ∃ t, s ⊆ t ∧ MeasurableSe... | [
1715,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1690,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.mul_star_self_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.44392\nE : Type u_1\nα : Type ?u.44398\ninst✝² : NonUnitalNormedRing E\ninst✝¹ : StarRing E\ninst✝ : CstarRing E\nx : E\n⊢ x * x⋆ = 0 ↔ x = 0",
"tactic": "simpa only [star_eq_zero, star_star] using @star_mul_self_eq_zero_iff _ _ _ _ (star x)"
... | [
149,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_adj | [] | [
1112,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
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Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biproduct.lift_eq | [
{
"state_after": "case w\nC : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nf : J → C\ninst✝ : HasBiproduct f\nT : C\ng : (j : J) → T ⟶ f j\n⊢ ∀ (j : J), lift g ≫ π (fun b => f b) j = (∑ j : J, g j ≫ ι f j) ≫ π (fun b => f b) j",
"state_before": "C : Type u\ninst✝³ : Cat... | [
219,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_ofReal_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.826990\nβ : Type ?u.826993\na✝ b c✝ d : ℝ≥0∞\nr p q : ℝ≥0\nc : ℝ\na : ℝ≥0∞\nh : 0 ≤ c\n⊢ ENNReal.toReal (ENNReal.ofReal c * a) = c * ENNReal.toReal a",
"tactic": "rw [ENNReal.toReal_mul, ENNReal.toReal_ofReal h]"
}
] | [
2255,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2253,
1
] |
Mathlib/Data/Set/Basic.lean | Set.disjoint_iff | [] | [
1518,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
11
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_bot_eq_top | [] | [
1657,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1656,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_toAddSubmonoid | [
{
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177,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Data/Set/Lattice.lean | Set.image2_iInter_subset_right | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort u_4\nι' : Sort ?u.252102\nι₂ : Sort ?u.252105\nκ : ι → Sort ?u.252110\nκ₁ : ι → Sort ?u.252115\nκ₂ : ι → Sort ?u.252120\nκ' : ι' → Sort ?u.252125\nf : α → β → γ\ns✝ : Set α\nt✝ : Set β\ns : Set α\nt : ι → Set β\n⊢ ∀ (x : α), x ∈ s → ∀ (y : β),... | [
1906,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1903,
1
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Mathlib/Algebra/Field/Basic.lean | div_sub_div_same | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.39149\nβ : Type ?u.39152\nK : Type u_1\ninst✝ : DivisionRing K\na✝ b✝ c✝ d a b c : K\n⊢ a / c - b / c = (a - b) / c",
"tactic": "rw [sub_eq_add_neg, ← neg_div, div_add_div_same, sub_eq_add_neg]"
}
] | [
153,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_over_two_pow_succ | [
{
"state_after": "x : ℝ\nn : ℕ\n⊢ sqrt (2 - sqrtTwoAddSeries 0 n) / 2 = sin (π / 2 ^ (n + 2))",
"state_before": "x : ℝ\nn : ℕ\n⊢ sin (π / 2 ^ (n + 2)) = sqrt (2 - sqrtTwoAddSeries 0 n) / 2",
"tactic": "symm"
},
{
"state_after": "x : ℝ\nn : ℕ\n⊢ sin (π / 2 ^ (n + 2)) * 2 = sqrt (2 - sqrtTwoAddSer... | [
777,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Std/Logic.lean | not_and_of_not_or_not | [] | [
342,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
342,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.Integrable.comp_div_left | [] | [
176,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_same | [] | [
807,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_prod | [
{
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475,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.104521\nm : MeasurableSpace α\nμ ν : Measure α\nf : ℕ → α → ℝ≥0∞\nhf : ∀ (n : ℕ), f n ∈ measurableLE μ ν\n⊢ (fun x => ⨆ (k : ℕ) (_ : k ≤ Nat.zero), f k x) ∈ measurableLE μ ν\n\ncase succ\nα : Type u_1\nβ : Type ?u.104521\nm✝ : MeasurableSpace α\nμ ν : Measu... | [
512,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
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Mathlib/Data/Sign.lean | sign_mul | [
{
"state_after": "no goals",
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"tactic": "rcases lt_trichotomy x 0 with (hx | hx | hx) <;> rcases lt_trichotomy y 0 with (hy | hy | hy) <;>\n simp [hx, hy, mul_pos_of_neg_of_neg, mul_neg_of_neg_... | [
403,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | coe_affineSpan | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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Mathlib/Data/List/Lattice.lean | List.cons_bagInter_of_neg | [
{
"state_after": "case nil\nα : Type u_1\nl l₁✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₁ : List α\nh : ¬a ∈ []\n⊢ List.bagInter (a :: l₁) [] = List.bagInter l₁ []\n\ncase cons\nα : Type u_1\nl l₁✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₁ : List α\nhead✝ : α\ntail✝ : List α\nh : ¬... | [
228,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.UnifIntegrable.add | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf g : ι → α → β\np : ℝ≥0∞\nhf : UnifIntegrable f p μ\nhg : UnifIntegrable g p μ\nhp : 1 ≤ p\nhf_meas : ∀ (i : ι), AEStronglyMeasurable (f i) μ\nhg_meas : ∀ (i : ι), AEStronglyMeasurabl... | [
125,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.inf | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.280281\nι : Type ?u.280284\ninst✝⁴ : Countable ι\nm0 : MeasurableSpace α\nμ : Measure α\nf g : α → β\ninst✝³ : TopologicalSpace β\ninst✝² : Zero β\ninst✝¹ : SemilatticeInf β\ninst✝ : ContinuousInf β\nhf : FinStronglyMeasurable f μ\nhg : FinStronglyMeasur... | [
1125,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
11
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.stabilizer_of_subMul.submonoid | [
{
"state_after": "case h\nS : Type u'\nT : Type u''\nR : Type u\nM : Type v\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\np : SubMulAction R M\nm : { x // x ∈ p }\nx✝ : R\n⊢ x✝ ∈ MulAction.Stabilizer.submonoid R m ↔ x✝ ∈ MulAction.Stabilizer.submonoid R ↑m",
"state_before": "S : Type u'\nT : Type u''\nR : Type... | [
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98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast?_isNone | [
{
"state_after": "no goals",
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.34045\nα : Type u\nβ : Type v\nγ : T... | [
779,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.coe_one | [] | [
685,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/Data/List/Sigma.lean | List.kerase_cons_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\ns : Sigma β\nl : List (Sigma β)\nh : a = s.fst\n⊢ kerase a (s :: l) = l",
"tactic": "simp [kerase, h]"
}
] | [
405,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.ediam_image_le_of_le | [] | [
159,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_span_singleton_mul_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.230454\ninst✝ : CommSemiring R\nI✝ J✝ K L : Ideal R\nx : R\nI J : Ideal R\n⊢ (∀ {zI : R}, zI ∈ I → zI ∈ span {x} * J) ↔ ∀ (zI : R), zI ∈ I → ∃ zJ, zJ ∈ J ∧ x * zJ = zI",
"tactic": "simp only [mem_span_singleton_mul]"
}
] | [
549,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Topology/Separation.lean | exists_nhds_disjoint_closure | [] | [
1007,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiable_neg_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.427827\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
452,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.tail_add | [] | [
482,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.coe_toSupHom | [] | [
1047,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.toList_empty | [] | [
3370,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3369,
1
] |
Std/Data/List/Lemmas.lean | List.get?_len_le | [] | [
511,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
509,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.I_mul_re | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.2411518\ninst✝ : IsROrC K\nz : K\n⊢ ↑re (I * z) = -↑im z",
"tactic": "simp only [I_re, zero_sub, I_im', zero_mul, mul_re]"
}
] | [
329,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.not | [] | [
716,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
11
] |
Mathlib/Order/SuccPred/Basic.lean | Order.lt_succ_iff | [] | [
337,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Topology/Separation.lean | continuousAt_of_tendsto_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : T1Space β\nf : α → β\na : α\nb : β\nh : Tendsto f (𝓝 a) (𝓝 b)\n⊢ Tendsto f (𝓝 a) (𝓝 (f a))",
"tactic": "rwa [eq_of_tendsto_nhds h]"
}
] | [
758,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftl'_add | [] | [
321,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_iff_forall_lintegral_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝⁶ : MeasurableSpace Ω\nR : Type ?u.153372\ninst✝⁵ : SMul R ℝ≥0\ninst✝⁴ : SMul R ℝ≥0∞\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nμ :... | [
552,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_nat_re | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.support_gen_of_gen' | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Monoid M\nS : Set (MonoidAlgebra R M)\nhS : adjoin R S = ⊤\n⊢ (↑(of R M) '' ⋃ (f : MonoidAlgebra R M) (_ : f ∈ S), ↑f.support) =\n ⋃ (f : MonoidAlgebra R M) (_ : f ∈ S), ↑(of R M) '' ↑f.support",
"state_before": "R : Type u_2\... | [
530,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.ordConnected | [] | [
238,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_eq_self_of_superset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3809\nι : Type ?u.3812\nM : Type u_2\nN : Type ?u.3818\ninst✝¹ : One M\ninst✝ : One N\ns t : Set α\nf g : α → M\na : α\nh1 : mulSupport f ⊆ s\nh2 : s ⊆ t\n⊢ mulSupport f ⊆ t",
"state_before": "α : Type u_1\nβ : Type ?u.3809\nι : Type ?u.3812\nM : Type u_2\nN : Typ... | [
118,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.le_iterate_pos_iff | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ x + ↑n * ↑m ≤ (↑f^[n]) x ↔ x + ↑m ≤ ↑f x",
"tactic": "simpa only [not_lt] using not_congr (f.iterate_pos_lt_iff hn)"
}
] | [
608,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_eq_bind₂ | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/List/Chain.lean | List.exists_chain_of_relationReflTransGen | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁ l₂ : List α\na b : α\nh : Relation.ReflTransGen r a b\n⊢ ∃ l, Chain r b l ∧ getLast (b :: l) (_ : b :: l ≠ []) = b\n\ncase refine'_2\nα : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁ l₂ : List α\na b : α\nh : Relation.ReflTransGe... | [
403,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/BinaryProducts.lean | hasBinaryCoproducts_of_hasInitial_and_pushouts | [] | [
196,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Sum.swap_map_inr | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Logic/Hydra.lean | Acc.cutExpand | [
{
"state_after": "case intro\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsIrrefl α r\na✝ a : α\nh : ∀ (y : α), r y a → Acc r y\nih : ∀ (y : α), r y a → Acc (CutExpand r) {y}\n⊢ Acc (CutExpand r) {a}",
"state_before": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsIrrefl α r\na : α\nhacc : Acc r a\n⊢ Acc (CutExpan... | [
152,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.toHamming_inj | [] | [
340,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.ne_zero | [] | [
70,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | lebesgue_number_lemma_of_metric | [] | [
2278,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2272,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.mono_null | [] | [
105,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableAt.const_mul | [] | [
485,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.ihom.ihom_adjunction_counit | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Bijective.existsUnique | [] | [
251,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
11
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.eq_of_le_of_finrank_le | [] | [
705,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
8
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.max_zero_left | [] | [
1004,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_False | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.321046\nγ : Type ?u.321049\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Finset α\na : α\n⊢ a ∈ filter (fun x => False) s ↔ a ∈ ∅",
"tactic": "simp [mem_filter, and_false_iff]"
}
] | [
2687,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2686,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_inter_le_ncard_left | [] | [
306,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Topology/Category/Profinite/CofilteredLimit.lean | Profinite.exists_clopen_of_cofiltered | [
{
"state_after": "case hT\nJ : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nU : Set ↑C.pt.toCompHaus.toTop\nhC : IsLimit C\nhU : IsClopen U\n⊢ ∀ (j : J), TopologicalSpace.IsTopologicalBasis ((fun j => {W | IsClopen W}) j)\n\nJ : Type u\ninst✝¹ : SmallCategory J\ninst✝... | [
124,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.swap_snd | [] | [
65,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.comp_sub | [] | [
944,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Topology/Inseparable.lean | specializes_of_eq | [] | [
176,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.hsum_add | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\nα : Type u_3\ns t : SummableFamily Γ R α\ng : Γ\n⊢ coeff (hsum (s + t)) g = coeff (hsum s + hsum t) g",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\... | [
1525,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.16765\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : M\nm n : ℕ\n⊢ a ^ (m * n) = (a ^ n) ^ m",
"tactic": "rw [Nat.mul_comm, pow_mul]"
}
] | [
136,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.sum_single | [] | [
120,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | SemiconjBy.zpow_right | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.114118\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group G\na x y : G\nh : SemiconjBy a x y\nn : ℕ\n⊢ SemiconjBy a (x ^ ↑n) (y ^ ↑n)",
"tactic": "simp [zpow_ofNat, h.pow_right n]"
}... | [
472,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | Differentiable.norm | [] | [
252,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.toEnd | [
{
"state_after": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ ValidFor (List.reverse r ++ l) [] { s := { data := List.reverseAux l r }, i := { byteIdx := utf8Len l + utf8Len r } }",
"state_before": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ ValidFor (List.reverse r ++ l) [] (Iterator... | [
589,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
587,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.polar_to_quadratic_form | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.369777\nR : Type u_1\nR₁ : Type ?u.369783\nM : Type u_2\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nB : BilinForm R M\nx y : M\n⊢ polar (fun x => bilin B x x) x y = bilin B x y + bilin B y x",
"tactic": "simp only [add_assoc, a... | [
726,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.toOrderAddMonoidHom_eq_coe | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.neg_apply | [] | [
1232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | sum_card_orderOf_eq_card_pow_eq_one | [
{
"state_after": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝² : Monoid G\ninst✝¹ : Fintype G\ninst✝ : DecidableEq G\nhn : n ≠ 0\nx✝ : ℕ\na✝² : x✝ ∈ Finset.filter (fun x => x ∣ n) (Finset.range (succ n))\ny✝ : ℕ\na✝¹ : y✝ ∈ Finset.filter (fun x => x ∣ n) (Finset.range (succ n))\na✝ : x✝ ≠ y✝\n⊢ Dis... | [
672,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | MeasureTheory.integral2_divergence_prod_of_hasFDerivWithinAt_off_countable | [
{
"state_after": "case inr\nE : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf g : ℝ × ℝ → E\nf' g' : ℝ × ℝ → ℝ × ℝ →L[ℝ] E\na₁ a₂ b₁ b₂ : ℝ\ns : Set (ℝ × ℝ)\nhs : Set.Countable s\nHcf : ContinuousOn f ([[a₁, b₁]] ×ˢ [[a₂, b₂]])\nHcg : ContinuousOn g ([[a₁, b₁]] ×ˢ [... | [
527,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_Ici | [] | [
1225,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/Order/Bounds/Basic.lean | BddBelow.bddAbove_image2_of_bddAbove | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Antitone (swap f b)\nh₁ : ∀ (a : α), Monotone (f a)\na : α\nha : a ∈ lowerBounds s\nb : β\nhb : b... | [
1530,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1527,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.embDomain_notin_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.218890\nι : Type ?u.218893\nM : Type u_3\nM' : Type ?u.218899\nN : Type ?u.218902\nP : Type ?u.218905\nG : Type ?u.218908\nH : Type ?u.218911\nR : Type ?u.218914\nS : Type ?u.218917\ninst✝¹ : Zero M\ninst✝ : Zero N\nf : α ... | [
868,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_bit1' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.39154\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : M\nn : ℕ\n⊢ a ^ bit1 n = (a * a) ^ n * a",
"tactic": "rw [bit1, pow_succ', pow_bit0']"
}
] | [
217,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
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