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/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_inj_left | [] | [
157,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | continuousOn_fract | [] | [
159,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Init/Algebra/Order.lean | ge_trans | [] | [
80,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Complex/Determinant.lean | Complex.det_conjAe | [
{
"state_after": "⊢ 1 * -1 - 0 * 0 = -1",
"state_before": "⊢ ↑LinearMap.det (AlgEquiv.toLinearMap conjAe) = -1",
"tactic": "rw [← LinearMap.det_toMatrix basisOneI, toMatrix_conjAe, Matrix.det_fin_two_of]"
},
{
"state_after": "no goals",
"state_before": "⊢ 1 * -1 - 0 * 0 = -1",
"tactic": ... | [
29,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearEquiv.coe_toContinuousLinearEquiv' | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.card_Ioc | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ card (Ioc a b) = ↑b - ↑a",
"tactic": "rw [← Nat.card_Ioc, ← map_valEmbedding_Ioc, card_map]"
}
] | [
90,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.iff_ideal_total | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\nK : Type ?u.525453\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\n⊢ ValuationRing R ↔ IsTotal (Ideal R) fun x x_1 => x ≤ x_1",
"tactic": "classical\nrefine' ⟨fun _ => ⟨le_total⟩, f... | [
299,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_ofNNRealHom | [] | [
465,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
9
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.lt_of_tendsto_zero_of_pos | [] | [
203,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.congr_arg | [] | [
610,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Topology/Bases.lean | Inducing.secondCountableTopology | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\nf : α → β\ninst✝ : SecondCountableTopology β\nhf : Inducing f\n⊢ SecondCountableTopology α",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\nf : α → ... | [
889,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
11
] |
Mathlib/Logic/Basic.lean | Exists.snd | [] | [
871,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.linearEquiv_smul_eq_map | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Std/Data/String/Lemmas.lean | String.isEmpty_iff | [] | [
166,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
165,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_eq_limsup_subtype | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.61523\nι : Type ?u.61526\ninst✝ : ConditionallyCompleteLattice α\nf : Filter β\nu : β → α\np : β → Prop\n⊢ sInf {a | ∀ᶠ (x : β) in f, p x → u x ≤ a} = sInf {a | ∀ᶠ (b : β) in f, ∀ (a_1 : { x // p x }), ↑a_1 = b → u ↑a_1 ≤ a}",
"state_before": "α : Ty... | [
418,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_mul_of_div_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.59378\nβ : Type ?u.59381\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : a / c = b\n⊢ a = b * c",
"tactic": "simp [← h]"
}
] | [
780,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Algebra/Group/ULift.lean | ULift.up_intCast | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_add_two_pi | [] | [
244,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.mod_coprime | [
{
"state_after": "m n a✝ b✝ c d : ℤ\na b : ℕ\nhab : Nat.coprime a b\nhgcd : Nat.gcd a b = 1\n⊢ ↑1 ≡ 1 [ZMOD ↑b]",
"state_before": "m n a✝ b✝ c d : ℤ\na b : ℕ\nhab : Nat.coprime a b\nhgcd : Nat.gcd a b = 1\n⊢ ↑a * Nat.gcdA a b + ↑b * Nat.gcdB a b ≡ 1 [ZMOD ↑b]",
"tactic": "rw [← Nat.gcd_eq_gcd_ab, hgcd]"... | [
303,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Topology/Algebra/UniformConvergence.lean | UniformOnFun.continuousSMul_induced_of_image_bounded | [
{
"state_after": "𝕜 : Type u_5\nα : Type u_1\nE : Type u_3\nH : Type u_2\nhom : Type u_4\ninst✝⁹ : NormedField 𝕜\ninst✝⁸ : AddCommGroup H\ninst✝⁷ : Module 𝕜 H\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : TopologicalSpace H\ninst✝³ : UniformSpace E\ninst✝² : UniformAddGroup E\ninst✝¹ : ContinuousS... | [
263,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.coe_add | [] | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.one_le_scalingConstantOf | [] | [
117,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/LinearAlgebra/Matrix/Diagonal.lean | Matrix.rank_diagonal | [
{
"state_after": "m : Type u_1\nn : Type ?u.179625\ninst✝⁴ : Fintype m\ninst✝³ : Fintype n\nK : Type u\ninst✝² : Field K\ninst✝¹ : DecidableEq m\ninst✝ : DecidableEq K\nw : m → K\nhu : univ ⊆ {i | w i = 0}ᶜ ∪ {i | w i = 0}\n⊢ rank (↑toLin' (diagonal w)) = ↑(Fintype.card { i // w i ≠ 0 })",
"state_before": "... | [
94,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.toEquiv_symm | [] | [
298,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.toSubring_inj | [] | [
247,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_preimage_left | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.subsingleton | [] | [
1240,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Functor.map_homCongr | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₁\ninst✝ : Category D\nF : C ⥤ D\nX Y X₁ Y₁ : C\nα : X ≅ X₁\nβ : Y ≅ Y₁\nf : X ⟶ Y\n⊢ F.map (↑(Iso.homCongr α β) f) = ↑(Iso.homCongr (F.mapIso α) (F.mapIso β)) (F.map f)",
"tactic": "simp"
}
] | [
181,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.image_vsub_product | [] | [
1451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.ptendsto'_of_ptendsto | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : α →. β\nl₁ : Filter α\nl₂ : Filter β\nh : PFun.Dom f ∈ l₁\n⊢ (∀ (s : Set β), s ∈ l₂ → PFun.core f s ∈ l₁) → ∀ (s : Set β), s ∈ l₂ → PFun.preimage f s ∈ l₁",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α →. β\nl₁ : Filter α\nl₂ : Filter β... | [
286,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ioo_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n => Ioo (↑n) (↑n + 1))",
"tactic": "simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)"
}
] | [
262,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_ball_comp | [] | [
627,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.charFn_eq_zero | [] | [
119,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_add_ofNat | [] | [
53,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
53,
9
] |
Std/Data/List/Lemmas.lean | List.eq_nil_iff_forall_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ l ⊆ [] ↔ ∀ (a : α), ¬a ∈ l",
"tactic": "simp [subset_def]"
}
] | [
269,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
268,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.mul_sub_right_distrib | [
{
"state_after": "no goals",
"state_before": "n m k : Nat\n⊢ (n - m) * k = n * k - m * k",
"tactic": "induction m with\n| zero => simp\n| succ m ih => rw [Nat.sub_succ, Nat.mul_pred_left, ih, succ_mul, Nat.sub_sub]; done"
},
{
"state_after": "no goals",
"state_before": "case zero\nn k : Nat\... | [
714,
87
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
711,
11
] |
Std/Data/Nat/Lemmas.lean | Nat.add_mul_mod_self_left | [
{
"state_after": "no goals",
"state_before": "x y z : Nat\n⊢ (x + y * z) % y = x % y",
"tactic": "match z with\n| 0 => rw [Nat.mul_zero, Nat.add_zero]\n| succ z => rw [mul_succ, ← Nat.add_assoc, add_mod_right, add_mul_mod_self_left (z := z)]"
},
{
"state_after": "no goals",
"state_before": "... | [
499,
92
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
496,
9
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Eigs.lean | Matrix.trace_eq_sum_roots_charpoly_of_splits | [
{
"state_after": "case inl\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_1\ninst✝ : Field R\nA : Matrix n n R\nhAps : Splits (RingHom.id R) (charpoly A)\nh : IsEmpty n\n⊢ trace A = Multiset.sum (roots (charpoly A))\n\ncase inr\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR ... | [
80,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.restrict | [] | [
314,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.μ_inv_naturalityₗ | [
{
"state_after": "C : Type u\ninst✝² : Category C\nM : Type u_2\ninst✝¹ : Category M\ninst✝ : MonoidalCategory M\nF : MonoidalFunctor M (C ⥤ C)\nm n m' : M\nf : m ⟶ m'\nX : C\n⊢ (F.obj n).map ((F.map f).app X) ≫ inv ((MonoidalFunctor.μIso F m' n).inv.app X) =\n inv ((MonoidalFunctor.μIso F m n).inv.app X) ≫ ... | [
174,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8700\nγ : Type ?u.8703\nδ : Type ?u.8706\nδ' : Type ?u.8709\nι : Sort ?u.8712\ns t u : Set α\nm : MeasurableSpace α\ns₁ s₂ : Set α\nh₁ : MeasurableSet s₁\nh₂ : MeasurableSet s₂\n⊢ MeasurableSet ((s₁ᶜ ∪ s₂ᶜ)ᶜ)",
"state_before": "α : Type u_1\nβ : Type ?u.8700\nγ : ... | [
204,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
11
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_ratCast | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.coe_toFinset | [] | [
638,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Std/Data/List/Lemmas.lean | List.filterMap_eq_map | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\n⊢ filterMap (some ∘ f) l = map f l",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\n⊢ filterMap (some ∘ f) = map f",
"tactic": "funext l"
},
{
"state_after": "no goals",
"state_before": "case h\nα : Type u_... | [
1167,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1166,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_permutations'Aux_comm | [
{
"state_after": "case nil\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\na b : α\n⊢ List.bind (permutations'Aux a []) (permutations'Aux b) ~ List.bind (permutations'Aux b []) (permutations'Aux a)\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\na b c : α\nl : List α\nih : List.bind (permutations'Aux a l) (p... | [
1297,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.ltOrEq_apply_left | [] | [
473,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Algebra/Group/Ext.lean | Monoid.ext | [
{
"state_after": "M : Type u\nm₁ m₂ : Monoid M\nh_mul : Mul.mul = Mul.mul\nthis : toMulOneClass = toMulOneClass\n⊢ m₁ = m₂",
"state_before": "M : Type u\nm₁ m₂ : Monoid M\nh_mul : Mul.mul = Mul.mul\n⊢ m₁ = m₂",
"tactic": "have : m₁.toMulOneClass = m₂.toMulOneClass := MulOneClass.ext h_mul"
},
{
... | [
43,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.trunc_C_mul_T | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\nr : R\nthis : Function.Injective Int.ofNat\n⊢ ↑trunc (↑C r * T n) = if 0 ≤ n then ↑(monomial (Int.toNat n)) r else 0",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\nr : R\n⊢ ↑trunc (↑C r * T n) = if 0 ≤ n then ↑(monomial (Int.toNat n)) r... | [
359,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.map_esymm | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nR : Type u_1\nτ : Type ?u.97879\nS : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S\ninst✝¹ : Fintype σ\ninst✝ : Fintype τ\nn : ℕ\nf : R →+* S\n⊢ ↑(map f) (esymm σ R n) = esymm σ S n",
"tactic": "simp_rw [esymm, map_sum, map_prod, m... | [
199,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | measure_le_lintegral_thickenedIndicatorAux | [
{
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.sinh | [] | [
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40
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1178,
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Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_bit0' | [] | [
179,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | nullMeasurableSet_of_null_frontier | [] | [
419,
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Mathlib/Data/Nat/Basic.lean | Nat.exists_lt_succ | [
{
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Mathlib/RingTheory/IntegralClosure.lean | normalizeScaleRoots_support | [
{
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_neg | [
{
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_sqrt | [
{
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{
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Mathlib/Data/Set/Image.lean | Set.range_image | [] | [
803,
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802,
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.join_cons_cons | [
{
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Mathlib/Analysis/Convex/Between.lean | sbtw_lineMap_iff | [
{
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_lt_of_le_right | [
{
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167,
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Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | HasStrictDerivAt.clog_real | [
{
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94,
95
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.inter | [] | [
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35
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Mathlib/Topology/Order.lean | continuous_generateFrom | [] | [
701,
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Mathlib/MeasureTheory/MeasurableSpace.lean | Subsingleton.measurable | [] | [
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38
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.inv_hom_id_tensor' | [
{
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386,
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.of_bot | [] | [
56,
54
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55,
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.coe_sSup_of_directedOn | [
{
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"tactic": "simp [mem_sSup_of_... | [
232,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
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Mathlib/Data/Nat/Digits.lean | Nat.three_dvd_iff | [
{
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] | [
596,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Dfinsupp.sum_inner | [
{
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwiseDisjoint_fiber | [] | [
355,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_of_left_mem | [
{
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264,
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Mathlib/Analysis/NormedSpace/Exponential.lean | Pi.exp_def | [] | [
560,
29
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557,
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Mathlib/Topology/UniformSpace/Compact.lean | HasCompactMulSupport.uniformContinuous_of_continuous | [] | [
242,
63
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240,
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Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.isBounded_iff_isVonNBounded | [] | [
233,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Algebra/Module/LinearMap.lean | AddMonoidHom.toNatLinearMap_injective | [
{
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753,
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src/lean/Init/Core.lean | Quotient.rel.refl | [] | [
1494,
28
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Std/Data/Int/Lemmas.lean | Int.le.dest_sub | [] | [
563,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
563,
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Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_diff | [
{
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254,
7
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251,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sub_le_self | [] | [
562,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.div_one_mul | [
{
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},
{
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352,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
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Mathlib/LinearAlgebra/Span.lean | Submodule.closure_le_toAddSubmonoid_span | [] | [
140,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | tsum_mul_left | [
{
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120,
92
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116,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.one_re | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.continuousOn | [
{
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888,
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883,
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Mathlib/Data/Int/Order/Units.lean | Int.sq_eq_one_of_sq_lt_four | [] | [
60,
47
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Mathlib/Order/Filter/Basic.lean | Filter.comap_eq_of_inverse | [
{
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2975,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2972,
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_C | [] | [
82,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
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Mathlib/Order/CompleteLattice.lean | iSup_split | [
{
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1424,
74
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1422,
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Mathlib/Data/Finset/Image.lean | Finset.image_subset_image | [
{
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"tactic": "simp only [subset_def, image_val, subset_dedup', dedup_subset... | [
441,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
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Mathlib/Data/Sym/Basic.lean | Sym.attach_mk | [] | [
432,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.complete_graph_degree | [
{
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"tactic": "erw [degree, ne... | [
1491,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.mul_mk | [] | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
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Mathlib/Order/Filter/CountableInter.lean | EventuallyEq.countable_bUnion | [] | [
100,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Data/Vector/Basic.lean | Vector.toList_reverse | [] | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
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Std/Data/String/Lemmas.lean | String.data_push | [] | [
26,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
26,
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Mathlib/Algebra/Module/Basic.lean | neg_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.299205\nR : Type ?u.299208\nk : Type ?u.299211\nS : Type ?u.299214\nM : Type u_1\nM₂ : Type ?u.299220\nM₃ : Type ?u.299223\nι : Type ?u.299226\ninst✝⁴ : Semiring R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : NoZeroSMulDivisors R M\ninst✝ ... | [
697,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_comap | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K✝ L : Subgroup G\nG' : Type u_1\ninst✝ : Group G'\nf : G' →* G\nK : Subgroup G'\n⊢ relindex (comap f H) K = relindex H (map f K)",
"tactic": "rw [relindex, subgroupOf, comap_comap, index_comap, ← f.map_range, K.subtype_rang... | [
93,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpTo.ofLe | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1255,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1254,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.mul_swap_involutive | [] | [
564,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
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