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/Logic/Function/Basic.lean | Function.Injective.comp_left | [] | [
148,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj₂.eq | [] | [
150,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
11
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.algebraMap_eq_inl | [] | [
596,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.comap_id_eq_map | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\nS : Type u\ninst✝¹ : CommRing S\nP : Type u\ninst✝ : CommRing P\nU V : Opens ↑(PrimeSpectrum.Top R)\niVU : V ⟶ U\ns : ↑((structureSheaf R).val.obj U.op)\np : { x // x ∈ V.op.unop }\n⊢ ↑(Localization.localRingHom (↑(PrimeSpectrum.comap (RingHom.id R)) ↑p).asIdea... | [
1179,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_singleton_le_iff_mem | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.28852\nA : Type ?u.28855\ninst✝¹ : MulOneClass M\ns : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS : Submonoid M\nm : M\np : Submonoid M\n⊢ closure {m} ≤ p ↔ m ∈ p",
"tactic": "rw [closure_le, singleton_subset_iff, SetLike.mem_coe]"
... | [
543,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.dvd_of_forall_prime_mul_dvd | [
{
"state_after": "case inl\nb : ℕ\nhdvd : ∀ (p : ℕ), Prime p → p ∣ 1 → p * 1 ∣ b\n⊢ 1 ∣ b\n\ncase inr\na b : ℕ\nhdvd : ∀ (p : ℕ), Prime p → p ∣ a → p * a ∣ b\nha : a ≠ 1\n⊢ a ∣ b",
"state_before": "a b : ℕ\nhdvd : ∀ (p : ℕ), Prime p → p ∣ a → p * a ∣ b\n⊢ a ∣ b",
"tactic": "obtain rfl | ha := eq_or_ne a... | [
470,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_induction' | [
{
"state_after": "M : Type u_1\nN : Type ?u.23218\nA : Type ?u.23221\ninst✝¹ : MulOneClass M\ns✝ : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS : Submonoid M\ns : Set M\np : (x : M) → x ∈ closure s → Prop\nHs : ∀ (x : M) (h : x ∈ s), p x (_ : x ∈ ↑(closure s))\nH1 : p 1 (_ : 1 ∈ closure s)\nHmul : ∀ (x : M) (hx ... | [
463,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_eq | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\nhb : 0 ≤ b\n⊢ a = b ∨ a = -b → abs a = b",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\nhb : 0 ≤ b\n⊢ abs a = b ↔ a = b ∨ a = -b",
"tactic": "refine' ⟨eq_or_eq_neg_of_abs_eq, _⟩"
},
... | [
322,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Topology/NhdsSet.lean | nhds_le_nhdsSet | [] | [
130,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | Irreducible.maximalIdeal_eq | [] | [
105,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_le_toIocMod | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocDiv hp a b • p ≤ toIcoDiv hp a b • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ... | [
706,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Algebra/GeomSum.lean | nat_sub_dvd_pow_sub_pow | [
{
"state_after": "case inl\nα : Type u\nx y n : ℕ\nh : y ≤ x\n⊢ x - y ∣ x ^ n - y ^ n\n\ncase inr\nα : Type u\nx y n : ℕ\nh : x < y\n⊢ x - y ∣ x ^ n - y ^ n",
"state_before": "α : Type u\nx y n : ℕ\n⊢ x - y ∣ x ^ n - y ^ n",
"tactic": "cases' le_or_lt y x with h h"
},
{
"state_after": "case inl\... | [
205,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type ?u.168671\nι : Type ?u.168674\nM : Type u_2\nM' : Type ?u.168680\nN : Type ?u.168683\nP : Type ?u.168686\nG : Type ?u.168689\nH✝ : Type ?u.168692\nR : Type ?u.168695\nS : Type ?u.168698\ninst✝ : AddCommMonoid M\nv v₁ v₂ : α →... | [
495,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.two_le_pi | [
{
"state_after": "no goals",
"state_before": "⊢ 0 < 2",
"tactic": "norm_num"
},
{
"state_after": "⊢ 1 ≤ π / 2",
"state_before": "⊢ 2 / 2 ≤ π / 2",
"tactic": "rw [div_self (two_ne_zero' ℝ)]"
},
{
"state_after": "no goals",
"state_before": "⊢ 1 ≤ π / 2",
"tactic": "exact on... | [
155,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientEquiv_symm_mk | [] | [
396,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.sigma_eq_iff_eq_comp_cast | [] | [
1004,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.intersecting_iff_pairwise_not_disjoint | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderBot α\ns t : Set α\na b c : α\nh : Intersecting s\n⊢ s ≠ {⊥}\n\ncase refine'_2\nα : Type u_1\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderBot α\ns t : Set α\na✝ b✝ c : α\nh : (Set.Pairwise s fun a b => ¬Disjoint a b) ∧ s ≠ {⊥}\n... | [
95,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_assoc | [] | [
351,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_bot | [
{
"state_after": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\n⊢ innerContent μ ⊥ ≤ 0",
"state_before": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\n⊢ innerContent μ ⊥ = 0",
"tactic": "refine' le_antisymm _ (zero_le _)"
},
{
"state_after": "G : Type w\ninst✝ : TopologicalSpa... | [
151,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.comp_apply | [] | [
959,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.induction_on | [] | [
1027,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
11
] |
Mathlib/Order/Filter/Bases.lean | FilterBasis.eq_iInf_principal | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.4090\nγ : Type ?u.4093\nι : Sort ?u.4096\nι' : Sort ?u.4099\nB : FilterBasis α\nthis : Directed (fun x x_1 => x ≥ x_1) fun s => 𝓟 ↑s\nU : Set α\n⊢ U ∈ FilterBasis.filter B ↔ U ∈ ⨅ (s : ↑B.sets), 𝓟 ↑s",
"state_before": "α : Type u_1\nβ : Type ?u.4090\nγ :... | [
193,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | nndist_vadd_vadd_le | [] | [
180,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factors_0 | [] | [
1437,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1436,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.terminates_of_LiftRel | [] | [
1119,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Isδ₀.eq_δ₀ | [
{
"state_after": "case intro\nC : Type ?u.2249\ninst✝² : Category C\ninst✝¹ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ Δ' Δ'' : SimplexCategory\nn : ℕ\nj : Fin (n + 2)\ninst✝ : Mono (SimplexCategory.δ j)\nhi : Isδ₀ (SimplexCategory.δ j)\n⊢ SimplexCategory.δ j = SimplexCategory.δ 0",
"state_befo... | [
68,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.BoundedContinuousFunction.inner_toLp | [
{
"state_after": "case h\nα : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasureSpace α\ninst✝² : BorelSpace α\n𝕜 : Type u_2\ninst✝¹ : IsROrC 𝕜\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nf g : α →ᵇ 𝕜\n⊢ (fun a =>\n inner (↑↑(↑(BoundedContinuousFunction.toLp 2 μ 𝕜) f) a) (↑↑(↑(BoundedContinuousFunc... | [
309,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_pow_even_mul_cos_pow_even | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn✝ m n : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x ^ (2 * m) * cos x ^ (2 * n)) =\n ∫ (x : ℝ) in a..b, ((1 - cos (2 * x)) / 2) ^ m * ((1 + cos (2 * x)) / 2) ^ n",
"tactic": "field_simp [pow_mul, sin_sq, cos_sq, ← sub_sub, (by ring : (2 : ℝ) - 1 = 1)]"
},
... | [
829,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_apply | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/ModelTheory/Ultraproducts.lean | FirstOrder.Language.Ultraproduct.funMap_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : α → Type u_2\nu : Ultrafilter α\nL : Language\ninst✝ : (a : α) → Structure L (M a)\nn : ℕ\nf : Functions L n\nx : Fin n → (a : α) → M a\n⊢ (funMap f fun i => Quotient.mk' (x i)) = Quotient.mk' fun a => funMap f fun i => x i a",
"tactic": "a... | [
83,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/List/Indexes.lean | List.oldMapIdxCore_eq | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nf✝ : ℕ → α → β\nn✝ : ℕ\nf : ℕ → α → β\nn : ℕ\n⊢ List.oldMapIdxCore f n [] = List.oldMapIdx (fun i a => f (i + n) a) []\n\ncase cons\nα : Type u\nβ : Type v\nf✝ : ℕ → α → β\nn✝ : ℕ\nhd : α\ntl : List α\nhl : ∀ (f : ℕ → α → β) (n : ℕ), List.oldMapIdxCore f n tl ... | [
54,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.mem_range_of_measure_ne_zero | [] | [
122,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/MinMax.lean | max_min_distrib_right | [] | [
120,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.ker_equiv | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nF : Type ?u.1774019\ninst✝² : Ring R\ninst✝¹ : Semiring S\nrc : RingHomClass F R S\nf✝ : F\nF' : Type u_1\ninst✝ : RingEquivClass F' R S\nf : F'\n⊢ ker f = ⊥",
"tactic": "simpa only [← injective_iff_ker_eq_bot] using Equiv... | [
2048,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2047,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.HasBinaryBiproducts.of_hasBinaryProducts | [] | [
384,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.T_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nm : ℤ\nn : ℕ\n⊢ T m ^ n = T (↑n * m)",
"tactic": "rw [T, T, single_pow n, one_pow, nsmul_eq_mul]"
}
] | [
190,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.ofSet_univ_eq_refl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.64088\nγ : Type ?u.64091\nδ : Type ?u.64094\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ns : Set α\nhs : IsOpen s\... | [
775,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.convergents'Aux_succ_none | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn✝ : ℕ\ninst✝ : DivisionRing K\ns : Stream'.Seq (Pair K)\nh : Stream'.Seq.head s = none\nn : ℕ\n⊢ convergents'Aux s (n + 1) = 0",
"tactic": "simp [convergents'Aux, h, convergents'Aux.match_1]"
}
] | [
182,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.coe_add | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | dslope_sub_smul | [] | [
86,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Analysis/Calculus/Deriv/Linear.lean | ContinuousLinearMap.hasDerivWithinAt | [] | [
65,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
11
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.inv_neg | [
{
"state_after": "q : ℚ\n⊢ (-(q.num /. ↑q.den))⁻¹ = -(q.num /. ↑q.den)⁻¹",
"state_before": "q : ℚ\n⊢ (-q)⁻¹ = -q⁻¹",
"tactic": "rw [← @num_den q]"
},
{
"state_after": "no goals",
"state_before": "q : ℚ\n⊢ (-(q.num /. ↑q.den))⁻¹ = -(q.num /. ↑q.den)⁻¹",
"tactic": "simp only [Rat.neg_def, ... | [
185,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | comap_measurable | [] | [
222,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasDerivAt_lineMap | [] | [
68,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality' | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\nD : Type u₁\ninst✝³ : Category D\ninst✝² : Preadditive D\ninst✝¹ : HasFiniteBiproducts D\nF : Mat_ C ⥤ D\ninst✝ : Functor.Additive F\nM N : Mat_ C\nf : M ⟶ N\n⊢ (additiveObjIsoBiproduct F M).inv ≫ F.map f... | [
435,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/List/Sigma.lean | List.dlookup_cons_eq | [] | [
184,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_add_eq_max | [
{
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_of_mem_closure' | [] | [
625,
56
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622,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_sup_map_of_injective | [] | [
419,
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Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | ContinuousMonoidHom.continuous_comp | [] | [
363,
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Mathlib/Analysis/Calculus/MeanValue.lean | image_norm_le_of_norm_deriv_right_lt_deriv_boundary | [] | [
297,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
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Std/Data/Nat/Lemmas.lean | Nat.mul_mod_left | [
{
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508,
35
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507,
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Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.toFun_eq_coe | [] | [
141,
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140,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomain.HeightOneSpectrum.irreducible | [] | [
1002,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_sub_nat_mul_pi | [] | [
1335,
32
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1334,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Submodule.mem_toSubalgebra | [] | [
563,
54
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Mathlib/Order/Closure.lean | LowerAdjoint.closure_union_closure_right | [] | [
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | ContinuousOn.integrableOn_Icc | [] | [
276,
40
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274,
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Mathlib/Data/Multiset/Basic.lean | Multiset.rel_refl_of_refl_on | [
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Mathlib/Data/Finset/NAry.lean | Set.Finite.toFinset_image2 | [
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565,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_congr | [
{
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_apply | [
{
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Mathlib/Data/Set/Finite.lean | Set.Finite.exists_finset | [
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... | [
118,
44
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115,
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Mathlib/Data/Stream/Init.lean | Stream'.append_append_stream | [
{
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535,
91
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531,
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_OrderMonoidWithZeroHom_id | [] | [
299,
6
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.image_closedBall_subset_compact | [] | [
153,
90
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150,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_nat_cast | [
{
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285,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_ratCast | [
{
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106,
29
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104,
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Mathlib/Topology/Connected.lean | locallyConnectedSpace_iff_open_connected_basis | [] | [
1117,
78
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1114,
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Mathlib/Order/Filter/Prod.lean | Filter.compl_mem_coprod | [
{
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494,
54
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492,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_zero_apply | [
{
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Mathlib/RingTheory/WittVector/WittPolynomial.lean | xInTermsOfW_aux | [
{
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298,
27
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294,
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Mathlib/Order/Bounds/Basic.lean | mem_upperBounds_image2_of_mem_upperBounds_of_mem_lowerBounds | [] | [
1407,
78
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1405,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_blsub | [] | [
1758,
6
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1756,
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Mathlib/Data/Finset/Card.lean | Finset.lt_wf | [] | [
712,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
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Mathlib/Data/PNat/Basic.lean | PNat.dvd_iff' | [
{
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{
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422,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
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Mathlib/RingTheory/WittVector/StructurePolynomial.lean | constantCoeff_wittStructureRat_zero | [
{
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363,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
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Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.comp_continuousOn_iff | [] | [
181,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_ofReal_eq_iff | [
{
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src/lean/Init/Data/String/Basic.lean | String.lt_next | [] | [
138,
41
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137,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.empty_vecAppend | [
{
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286,
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Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.toMatrix_row_sum_one | [
{
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60,
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59,
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Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingSeminorm.apply_one | [] | [
143,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.ext | [] | [
191,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_sSup_iff | [] | [
592,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.is_linear_image | [] | [
141,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_add_of_natDegree_lt_right | [
{
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180,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_nhds_iff | [] | [
653,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.Disjoint.cycleOf_mul_distrib | [
{
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1128,
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Mathlib/Data/Finset/Basic.lean | Finset.cons_eq_insert | [
{
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}
] | [
1082,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/SubsetProperties.lean | compactCovering_subset | [] | [
1313,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Gcd.lean | Nat.coprime_one_right | [] | [
359,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
359,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.induction₂ | [
{
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999,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_top | [
{
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] | [
1338,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
9
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Mathlib/Data/Real/NNReal.lean | NNReal.div_le_div_left_of_le | [] | [
855,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.centralizer_toSubmonoid | [] | [
857,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.bicone_π | [] | [
396,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Real.diam_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.561104\nβ : Type ?u.561107\nγ : Type ?u.561110\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : a ≤ b\n⊢ Metric.diam (Icc a b) = b - a",
"tactic": "simp [Metric.diam, ENNReal.toReal_ofReal (sub_nonneg.2 h)]"
}
] | [
1556,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1555,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.map_le_smul_top | [
{
"state_after": "case intro.intro\nR : Type u\nM : Type v\nF : Type ?u.56157\nG : Type ?u.56160\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI✝ J : Ideal R\nN P : Submodule R M\nI : Ideal R\nf : R →ₗ[R] M\ny : R\nhy : y ∈ ↑I\n⊢ ↑f y ∈ I • ⊤",
"state_before": "R : Type u\nM : Type... | [
169,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_bot | [] | [
905,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
11
] |
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