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/Algebra/Group/Commute.lean | Commute.units_inv_right | [] | [
223,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_congr_set_ae | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.3053\nE : Type u_2\nF : Type ?u.3059\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nhst : s =ᵐ[μ] t\n⊢ (∫ (x : α... | [
96,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Order/Filter/Basic.lean | Filter.map_iInf_eq | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ... | [
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2488,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.tendsto_abs_tan_atTop | [] | [
50,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.le_arcsin_iff_sin_le' | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : x ∈ Ioc (-(π / 2)) (π / 2)\n⊢ x ≤ arcsin y ↔ sin x ≤ y",
"tactic": "rw [← neg_le_neg_iff, ← arcsin_neg, arcsin_le_iff_le_sin' ⟨neg_le_neg hx.2, neg_lt.2 hx.1⟩,\n sin_neg, neg_le_neg_iff]"
}
] | [
172,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Combinatorics/Composition.lean | Composition.blocks_pos' | [] | [
194,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_ofReal_atTop | [] | [
193,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_neg | [
{
"state_after": "case a.h\nl : Type u_3\nm : Type u_4\nn : Type u_2\no : Type u_5\np : Type ?u.30648\nq : Type ?u.30651\nm' : o → Type ?u.30656\nn' : o → Type ?u.30661\np' : o → Type ?u.30666\nR : Type u_1\nS : Type ?u.30672\nα : Type ?u.30675\nβ : Type ?u.30678\ninst✝ : Neg R\nA : Matrix n l R\nB : Matrix n m... | [
234,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.coe_comp | [] | [
647,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.constantCoeff_C | [
{
"state_after": "no goals",
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"tactic": "classical simp [constantCoe... | [
871,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | LinearEquiv.uniformEmbedding | [] | [
2151,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2143,
11
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Mathlib/Data/Matrix/Basic.lean | Matrix.reindex_updateColumn | [] | [
2924,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2921,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Relabelling.mk_leftMovesEquiv | [] | [
1043,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
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Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_coe | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | AntitoneOn.mul_strictAnti' | [] | [
1510,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1506,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_mul' | [] | [
384,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Control/Traversable/Instances.lean | Sum.naturality | [
{
"state_after": "no goals",
"state_before": "σ : Type u\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nη : ApplicativeTransformation F G\nα : Type u_1\nβ : Type u\nf : α → F β\nx : σ ⊕ α\n⊢ (fun {α} => ApplicativeTransforma... | [
193,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
11
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.eq_zero_of_fst_eq_zero | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.370358\ninst✝¹ : CommSemiring P\ninst✝ : IsLocalization M S\nz : S\nx : R\ny : { x // x ∈ M }\nh : z * ↑(algebraMap R S) ↑y = 0\nhx : x = 0\n⊢ z = 0",
"state_bef... | [
224,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.sInf_gc | [
{
"state_after": "P : Type u_1\ninst✝ : CompleteSemilatticeInf P\nF✝ : PFilter P\nx : P\nF : (PFilter P)ᵒᵈ\n⊢ ↑toDual (principal x) ≤ F ↔ ∀ (b : P), b ∈ ↑ofDual F → x ≤ b",
"state_before": "P : Type u_1\ninst✝ : CompleteSemilatticeInf P\nF✝ : PFilter P\nx : P\nF : (PFilter P)ᵒᵈ\n⊢ (fun x => ↑toDual (princip... | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_arrow | [] | [
498,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
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Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.costructuredArrow_yoneda_equivalence_naturality | [
{
"state_after": "case h_obj\nC : Type u\ninst✝ : Category C\nF : C ⥤ Type w\nF₁ F₂ : Cᵒᵖ ⥤ Type v\nα : F₁ ⟶ F₂\n⊢ ∀ (X : (Functor.Elements F₁)ᵒᵖ),\n (Functor.op (map α) ⋙ toCostructuredArrow F₂).obj X = (toCostructuredArrow F₁ ⋙ CostructuredArrow.map α).obj X\n\ncase h_map\nC : Type u\ninst✝ : Category C\nF... | [
283,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.left_mem_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4365\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ a ∈ Ioc a b ↔ False",
"tactic": "simp [lt_irrefl]"
}
] | [
200,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Std/Data/List/Lemmas.lean | List.range_eq_nil | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ range n = [] ↔ n = 0",
"tactic": "rw [← length_eq_zero, length_range]"
}
] | [
1904,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1903,
9
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_mul_eq_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.68899\nι : Type ?u.68902\nM : Type u_2\nN : Type ?u.68908\ninst✝ : MulOneClass M\ns t : Set α\nf✝ g✝ : α → M\na : α\nf g : α → M\nh : Disjoint (mulSupport f) (mulSupport g)\nx : α\nhx : x ∈ mulSupport g\n⊢ (f * g) x = g x",
"state_before": "α : Type u_1\nβ : Type ... | [
458,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_const | [] | [
695,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Order/SymmDiff.lean | Pi.symmDiff_def | [] | [
854,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.zpow_pos | [
{
"state_after": "case ofNat\nα : Type ?u.409403\nβ : Type ?u.409406\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ 0\nh'a : a ≠ ⊤\na✝ : ℕ\n⊢ 0 < a ^ Int.ofNat a✝\n\ncase negSucc\nα : Type ?u.409403\nβ : Type ?u.409406\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ 0\nh'a : a ≠ ⊤\na✝ : ℕ\n⊢ 0 < a ^ Int.negSucc a✝",
"state_... | [
1865,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1862,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.equiv_symm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_3\nF : Type ?u.3085209\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_1\nι' : Type u_4\nι'' : Type ?u... | [
1425,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1421,
1
] |
Mathlib/Topology/Order/Basic.lean | nhds_eq_iInf_abs_sub | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : OrderTopology α\nl : Filter β\nf g : β → α\na : α\n⊢ ((⨅ (b : α) (_ : b ∈ Iio a), 𝓟 (Ioi b)) ⊓ ⨅ (b : α) (_ : b ∈ Ioi a), 𝓟 (Iio b)) =\n (⨅ (x : α) (_ : x > 0), 𝓟 {a_1 | -x < a ... | [
1856,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1852,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_id | [] | [
1176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.snorm_indicator_eq_snorm_restrict | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.658895\nF : Type u_2\nG : Type ?u.658901\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ns : Set α\nhs✝ : MeasurableSet s\nc : E\nf✝ : α → E\nhf : AEStro... | [
668,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictAnti.mul_const' | [] | [
1422,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1421,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.zero_rpow_of_pos | [
{
"state_after": "y : ℝ\nh : 0 < y\n⊢ Option.some 0 ^ y = Option.some 0",
"state_before": "y : ℝ\nh : 0 < y\n⊢ 0 ^ y = 0",
"tactic": "rw [← ENNReal.coe_zero, ← ENNReal.some_eq_coe]"
},
{
"state_after": "no goals",
"state_before": "y : ℝ\nh : 0 < y\n⊢ (if 0 = 0 ∧ y < 0 then ⊤ else ↑(NNReal.rp... | [
327,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.finSuccEquiv_X_succ | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.994751\na a' a₁ a₂ : R\ne : ℕ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\nn : ℕ\nj : Fin n\n⊢ ↑(finSuccEquiv R n) (X (Fin.succ j)) = ↑Polynomial.C (X j)",
"tactic": "simp"
}
] | [
362,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.uniformContinuous | [] | [
269,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
11
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_coe_iff | [] | [
1282,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1281,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_order | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : Preorder α\nt : OrderTopology α\nf : β → α\na : α\nx : Filter β\n⊢ ((∀ (i : α), i ∈ Iio a → ∀ᶠ (a : β) in x, f a ∈ Ioi i) ∧ ∀ (i : α), i ∈ Ioi a → ∀ᶠ (a : β) in x, f a ∈ Iio i) ↔\n (∀ (a' : α), a' < a → ∀ᶠ (b : β) in x... | [
935,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.image_fst_graph | [] | [
101,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/PrimeIdeal.lean | Order.Ideal.PrimePair.disjoint | [] | [
78,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
11
] |
Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.comp_val | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Computability/Language.lean | Language.mul_self_kstar_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.121636\nγ : Type ?u.121639\nl✝ m : Language α\na b x : List α\nl : Language α\n⊢ l∗ * l = l * l∗",
"tactic": "simp only [kstar_eq_iSup_pow, mul_iSup, iSup_mul, ← pow_succ, ← pow_succ']"
}
] | [
281,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_lpBcfₗᵢ | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.mono_left | [] | [
74,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.union_quotToDoset | [
{
"state_after": "case h\nG : Type u_1\ninst✝¹ : Group G\nα : Type ?u.56988\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\nx : G\n⊢ (x ∈ ⋃ (q : Quotient ↑H ↑K), quotToDoset H K q) ↔ x ∈ Set.univ",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.56988\ninst✝ : Mul α\nJ : Subgroup G\ng ... | [
170,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | Commute.list_prod_right | [
{
"state_after": "case nil\nι : Type ?u.71204\nα : Type ?u.71207\nM : Type u_1\nN : Type ?u.71213\nP : Type ?u.71216\nM₀ : Type ?u.71219\nG : Type ?u.71222\nR : Type ?u.71225\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl✝ l₁ l₂ : List M\na : M\nl : List M\ny : M\nh✝ : ∀ (x : M), x ∈ l → Commute y x... | [
252,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cofork.IsColimit.hom_ext | [] | [
427,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/List/Range.lean | List.nthLe_range'_1 | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn m i : ℕ\nH : i < length (range' n m)\n⊢ nthLe (range' n m) i H = n + i",
"tactic": "simp"
}
] | [
65,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | SubsemiringClass.coe_pow | [
{
"state_after": "case zero\nR✝ : Type u\nS : Type v\nT : Type w\ninst✝⁴ : NonAssocSemiring R✝\nM : Submonoid R✝\ninst✝³ : SetLike S R✝\nhSR : SubsemiringClass S R✝\ns : S\nR : Type u_1\ninst✝² : Semiring R\ninst✝¹ : SetLike S R\ninst✝ : SubsemiringClass S R\nx : { x // x ∈ s }\n⊢ ↑(x ^ Nat.zero) = ↑x ^ Nat.zer... | [
122,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Std/Data/String/Lemmas.lean | String.validFor_toSubstring | [
{
"state_after": "no goals",
"state_before": "s : String\n⊢ (toSubstring s).str.data = [] ++ s.data ++ []",
"tactic": "simp [toSubstring]"
},
{
"state_after": "no goals",
"state_before": "s : String\n⊢ (toSubstring s).stopPos.byteIdx = utf8Len [] + utf8Len s.data",
"tactic": "simp [toSub... | [
801,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
800,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sdiff_comm | [] | [
632,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.topologicalSpace_eq | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.57789\nι : Type ?u.57792\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n𝔖 : Set (Set α)\n⊢ (⨅ (i : Set α) (_ : i ∈ 𝔖), TopologicalSpace.induced (restrict i) UniformSpace.toTopologicalSpace) =\n ⨅ (s : Set α) (_ : s ∈ 𝔖),\n ... | [
633,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
11
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.interpolate_eq_iff_values_eq_on | [] | [
371,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_subset_iUnion_const | [] | [
1298,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Subsemigroup.center_eq_top | [] | [
188,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Algebra/Group/Prod.lean | MulHom.comp_coprod | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.44652\nB : Type ?u.44655\nG : Type ?u.44658\nH : Type ?u.44661\nM : Type u_3\nN : Type u_4\nP : Type u_2\ninst✝³ : Mul M\ninst✝² : Mul N\ninst✝¹ : CommSemigroup P\nf✝ : M →ₙ* P\ng✝ : N →ₙ* P\nQ : Type u_1\ninst✝ : CommSemigroup Q\nh : P →ₙ* Q\nf : M ... | [
434,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map.unique | [
{
"state_after": "case mk\nα : Type u\nL✝ L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\nf : α → β\nx y : FreeGroup α\ng : FreeGroup α →* FreeGroup β\nhg : ∀ (x : α), ↑g (FreeGroup.of x) = FreeGroup.of (f x)\nx✝ : FreeGroup α\nL : List (α × Bool)\n⊢ ↑g (Quot.mk Red.Step L) = ↑(map f) (Quot.mk Red.Step L)",
"sta... | [
842,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.cmpLT.trans_r | [] | [
37,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
36,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_comm | [] | [
2901,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2900,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.last_pos | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ 0 < last (n + 1)",
"tactic": "simp [lt_iff_val_lt_val]"
}
] | [
545,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/CategoryTheory/Bicategory/Functor.lean | CategoryTheory.Pseudofunctor.to_oplax_mapComp | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Order/SemiconjSup.lean | Function.sSup_div_semiconj | [] | [
120,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_zero_right | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ninst✝ : (j : Fin (n + 1)) → Zero (α j)\ni : Fin (n + 1)\nx : α i\n⊢ Pi.single i x i = x ∧ 0 = fun j => Pi.single i x (↑(succAbove i) j)",
"tactic": "simp [succAbove_ne, Pi.zero_def]"
}
] | [
756,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castPred_last | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ ↑(castPred (last (n + 1))) = ↑(last n)",
"tactic": "simp [castPred, predAbove, castSucc_lt_last]"
}
] | [
2319,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2318,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_eq_toNNReal_iff | [] | [
380,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.sound | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝ : Category C\nr : HomRel C\na b : C\nf₁ f₂ : a ⟶ b\nh : r f₁ f₂\n⊢ (functor r).map f₁ = (functor r).map f₂",
"tactic": "simpa using Quot.sound (CompClosure.intro (𝟙 a) f₁ f₂ (𝟙 b) h)"
}
] | [
141,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.compl_apply | [
{
"state_after": "V : Type u_2\nα : Type u_1\nβ : Type ?u.12780\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq V\nA : Matrix V V α\ninst✝¹ : Zero α\ninst✝ : One α\ni j : V\n⊢ (if i = j then 0 else if A i j = 0 then 1 else 0) = 0 ∨ (if i = j then 0 else if A i j = 0 then 1 else 0) = 1",
"state_before": "V : T... | [
114,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_self_subset_prod_self | [] | [
90,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | interior_closedBall' | [
{
"state_after": "case inl\nα : Type ?u.306784\nβ : Type ?u.306787\nγ : Type ?u.306790\nι : Type ?u.306793\ninst✝⁶ : NormedField α\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace α E\nF : Type ?u.306886\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace α F\ninst✝¹ : NormedSpace ℝ E\ninst✝ ... | [
387,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/NormedSpace/DualNumber.lean | DualNumber.exp_eps | [] | [
38,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.add_im | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | subset_interior_mul' | [] | [
1311,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_inv_distrib | [] | [
1807,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1806,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.apply_coe_mem_map | [] | [
1426,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1425,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_iUnion₂ | [] | [
247,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_singleton_mul_left_mono | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.238401\ninst✝¹ : CommSemiring R\nI J K L : Ideal R\ninst✝ : IsDomain R\nx : R\nhx : x ≠ 0\n⊢ I * span {x} ≤ J * span {x} ↔ I ≤ J",
"tactic": "simpa only [mul_comm I, mul_comm J] using span_singleton_mul_right_mono hx"
}
] | [
576,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.image_symm | [] | [
456,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace ℝ V\ninst✝⁵ : MetricSpace P\ninst✝⁴ : NormedAddTorsor V P\ns₁ s₂ : AffineSubspace ℝ P\ninst✝³ : Nonempty { x // x ∈ s₁ }\ninst✝² : Nonempty { x // x ∈ s₂ }\ninst✝¹ : CompleteSpace { x // x ∈ direction s₁ }\ni... | [
613,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_val_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.103482\nγ : Type ?u.103485\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝ b a : α\ns : Finset α\nh : ¬a ∈ s\n⊢ (insert a s).val = a ::ₘ s.val",
"tactic": "rw [insert_val, ndinsert_of_not_mem h]"
}
] | [
1056,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_cons | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.IsPartition.pairwiseDisjoint | [] | [
225,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullbackIsoProdSubtype_inv_fst | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nX Y Z : TopCat\nf : X ⟶ Z\ng : Y ⟶ Z\n⊢ (pullbackIsoProdSubtype f g).inv ≫ pullback.fst = pullbackFst f g",
"tactic": "simp [pullbackCone, pullbackIsoProdSubtype]"
}
] | [
103,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.inv_tendsto_zero | [] | [
154,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.get_equiv | [] | [
1018,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.pnatDen_one | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.Mon_tensor_one_mul | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nM N : Mon_ C\n⊢ (((λ_ (𝟙_ C)).inv ⊗ 𝟙 (M.X ⊗ N.X)) ≫ ((M.one ⊗ N.one) ⊗ 𝟙 (M.X ⊗ N.X))) ≫\n tensor_μ C (M.X, N.X) (M.X, N.X) ≫ (M.mul ⊗ N.mul) =\n (λ_ (M.X ⊗ N.X)).hom",
"state_before": "C ... | [
418,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Quotient.lean | MeasurePreservingQuotientGroup.mk' | [
{
"state_after": "G : Type u_1\ninst✝¹² : Group G\ninst✝¹¹ : MeasurableSpace G\ninst✝¹⁰ : TopologicalSpace G\ninst✝⁹ : TopologicalGroup G\ninst✝⁸ : BorelSpace G\nμ : MeasureTheory.Measure G\nΓ : Subgroup G\n𝓕 : Set G\nh𝓕 : IsFundamentalDomain { x // x ∈ ↑Subgroup.opposite Γ } 𝓕\ninst✝⁷ : Countable { x // x ∈... | [
159,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Order/Basic.lean | eq_of_ge_of_not_gt | [] | [
425,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Topology/Order/Basic.lean | frontier_Iic | [] | [
2341,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2340,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.coe_pureOneHom | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | ContinuousMonoidHom.inducing_toContinuousMap | [] | [
281,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_surjective | [
{
"state_after": "R✝ : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ✝ : Type ?u.315261\na✝ a' a₁ a₂ : R✝\ne : ℕ\nn m : σ✝\ns : σ✝ →₀ ℕ\ninst✝³ : CommSemiring R✝\ninst✝² : CommSemiring S₁\np✝ q : MvPolynomial σ✝ R✝\nR : Type u_1\ninst✝¹ : CommSemiring R\nσ : Type u_2\ninst✝ : IsEmpty σ\np : MvPolynomial σ R\n... | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.model_distinctConstantsTheory | [
{
"state_after": "L : Language\nL' : Language\nM✝ : Type w\nN : Type ?u.854555\nP : Type ?u.854558\ninst✝³ : Structure L M✝\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nT : Theory L\nM : Type w\ninst✝ : Structure (L[[α]]) M\ns : Set α\n⊢ (∀ (φ : Sentence (L[[α]])) (x x_1 : α... | [
1088,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.toMeasure_zero | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.prime_C_iff | [
{
"state_after": "R : Type u\nS : Type ?u.257711\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nr : R\nhr : Prime r\n⊢ Prime (↑C r)",
"state_before": "R : Type u\nS : Type ?u.257711\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRi... | [
762,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Algebra/Order/Kleene.lean | add_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17357\nι : Type ?u.17360\nπ : ι → Type ?u.17365\ninst✝ : IdemSemiring α\na✝ b c a : α\n⊢ a + a = a",
"tactic": "simp"
}
] | [
144,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.smul_def | [] | [
476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ico_of_Ioo | [] | [
254,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_inv_eq_ite | [
{
"state_after": "case pos\nx : ℂ\nhx : x = 0\n⊢ log x⁻¹ = if arg x = π then -↑(starRingEnd ℂ) (log x) else -log x\n\ncase neg\nx : ℂ\nhx : ¬x = 0\n⊢ log x⁻¹ = if arg x = π then -↑(starRingEnd ℂ) (log x) else -log x",
"state_before": "x : ℂ\n⊢ log x⁻¹ = if arg x = π then -↑(starRingEnd ℂ) (log x) else -log ... | [
133,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_right_strictMono | [] | [
105,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Subsets and Splits
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