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/Data/Sym/Sym2.lean | Sym2.mem_fromRel_irrefl_other_ne | [] | [
523,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_union_inter_subset | [
{
"state_after": "α : Type u_1\nα' : Type ?u.105175\nβ : Type u_2\nβ' : Type ?u.105181\nγ : Type ?u.105184\nγ' : Type ?u.105187\nδ : Type ?u.105190\nδ' : Type ?u.105193\nε : Type ?u.105196\nε' : Type ?u.105199\nζ : Type ?u.105202\nζ' : Type ?u.105205\nν : Type ?u.105208\ninst✝⁹ : DecidableEq α'\ninst✝⁸ : Decida... | [
548,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom | [] | [
426,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.mul_omega_opow_opow | [
{
"state_after": "case pos\na b : Ordinal\na0 : 0 < a\nh : a < ω ^ ω ^ b\nb0 : b = 0\n⊢ a * ω ^ ω ^ b = ω ^ ω ^ b\n\ncase neg\na b : Ordinal\na0 : 0 < a\nh : a < ω ^ ω ^ b\nb0 : ¬b = 0\n⊢ a * ω ^ ω ^ b = ω ^ ω ^ b",
"state_before": "a b : Ordinal\na0 : 0 < a\nh : a < ω ^ ω ^ b\n⊢ a * ω ^ ω ^ b = ω ^ ω ^ b",... | [
376,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.has_seq_basis | [] | [
1070,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/CategoryTheory/Abelian/RightDerived.lean | CategoryTheory.NatTrans.rightDerived_eq | [
{
"state_after": "C : Type u\ninst✝⁶ : Category C\nD : Type u_2\ninst✝⁵ : Category D\ninst✝⁴ : Abelian C\ninst✝³ : HasInjectiveResolutions C\ninst✝² : Abelian D\nF G : C ⥤ D\ninst✝¹ : Functor.Additive F\ninst✝ : Functor.Additive G\nα : F ⟶ G\nn : ℕ\nX : C\nP : InjectiveResolution X\n⊢ (Functor.rightDerivedObjIs... | [
172,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_lt_toNNRat_iff_of_nonneg | [] | [
374,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.constantCoeff_C | [] | [
1538,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1537,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | UniformContinuous.zpow_const | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : Group α\ninst✝¹ : UniformGroup α\ninst✝ : UniformSpace β\nf : β → α\nhf : UniformContinuous f\nn : ℕ\n⊢ UniformContinuous fun x => f x ^ n",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : Group α\... | [
143,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.ext_iff | [] | [
242,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.const_add | [] | [
269,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
8
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasStrictFDerivAt.mul_const | [
{
"state_after": "case h.e'_10\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type ?u.871792\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type ?u.871887\ninst✝⁷ : NormedAddCommGroup G\ninst✝⁶ : NormedSpace 𝕜 ... | [
396,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/List/Palindrome.lean | List.Palindrome.map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : List α\nf : α → β\np : Palindrome l\n⊢ reverse (map f l) = map f l",
"tactic": "rw [← map_reverse, p.reverse_eq]"
}
] | [
77,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixingSubgroup_union | [] | [
146,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.valuation_map_add | [
{
"state_after": "case pos\np : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\nhxy : x + y ≠ 0\nhx : x = 0\n⊢ min (valuation x) (valuation y) ≤ valuation (x + y)\n\ncase neg\np : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\nhxy : x + y ≠ 0\nhx : ¬x = 0\n⊢ min (valuation x) (valuation y) ≤ valuation (x + y)",
"state_b... | [
1087,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.symmetry | [] | [
1126,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineSubspace.subtypeₐᵢ_linear | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.continuous_symm | [] | [
146,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
11
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.append_left | [
{
"state_after": "α : Type u\nL L₁ L₂ L₃ L₄ x✝¹ L₁✝ L₂✝ : List (α × Bool)\nx✝ : α\nb✝ : Bool\n⊢ Step (x✝¹ ++ L₁✝ ++ (x✝, b✝) :: (x✝, !b✝) :: L₂✝) (x✝¹ ++ L₁✝ ++ L₂✝)",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ x✝¹ L₁✝ L₂✝ : List (α × Bool)\nx✝ : α\nb✝ : Bool\n⊢ Step (x✝¹ ++ (L₁✝ ++ (x✝, b✝) :: (x✝, !b✝) ::... | [
137,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_dvd_coeff | [
{
"state_after": "case pos\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nn : ℕ\nh : n ∈ support p\n⊢ content p ∣ coeff p n\n\ncase neg\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nn : ℕ\nh : ¬n ∈ support p\n... | [
91,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.sum_Ico_Ico_comm | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na✝ : α\ng f✝ : α → β\ninst✝¹ : CommMonoid β\nM : Type u_1\ninst✝ : AddCommMonoid M\na b : ℕ\nf : ℕ → ℕ → M\n⊢ ∑ x in Finset.sigma (Ico a b) fun i => Ico i b, f x.fst x.snd =\n ∑ x in Finset.sigma (Ico a b) fun j => Ico a (j + 1), f x.s... | [
136,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.toPEquiv_mul_matrix | [
{
"state_after": "case a.h\nk : Type ?u.14630\nl : Type ?u.14633\nm : Type u_1\nn : Type u_2\nα : Type v\ninst✝² : Fintype m\ninst✝¹ : DecidableEq m\ninst✝ : Semiring α\nf : m ≃ m\nM : Matrix m n α\ni : m\nj : n\n⊢ (toMatrix (Equiv.toPEquiv f) ⬝ M) i j = M (↑f i) j",
"state_before": "k : Type ?u.14630\nl : ... | [
108,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.eventually_forall_of_forall_eventually | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Type ?u.29509\nπ : ι → Type ?u.29514\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nx₀ : α\nK : Set β\nhK : IsCompact K\nP : α → β → Prop\nhP : ∀ (y : β), y ∈ K → ∀ᶠ (z : α × β) in 𝓝 (x₀, y), P z.fst z.snd\n⊢ ∀ᶠ (x : α) in 𝓝... | [
387,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.sum_toMatrix_smul_self | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type u_4\nκ : Type ?u.260003\nκ' : Type ?u.260006\nR : Type u_3\nM : Type u_2\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nR₂ : Type ?u.260199\nM₂ : Type ?u.260202\ninst✝³ : CommRing R₂\ninst✝² : AddCommGroup M₂\nin... | [
121,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.coe_int_cast | [
{
"state_after": "case zero\na : ℤ\n⊢ ↑↑a = a % ↑Nat.zero\n\ncase succ\na : ℤ\nn✝ : ℕ\n⊢ ↑↑a = a % ↑(Nat.succ n✝)",
"state_before": "n : ℕ\na : ℤ\n⊢ ↑↑a = a % ↑n",
"tactic": "cases n"
},
{
"state_after": "case zero\na : ℤ\n⊢ ↑a = a",
"state_before": "case zero\na : ℤ\n⊢ ↑↑a = a % ↑Nat.zero",... | [
496,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Order/Hom/Basic.lean | map_inv_le_iff | [
{
"state_after": "case h.e'_2.h.e'_3\nF : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.27241\nδ : Type ?u.27244\ninst✝² : LE α\ninst✝¹ : LE β\ninst✝ : OrderIsoClass F α β\nf : F\na : α\nb : β\n⊢ b = ↑f (EquivLike.inv f b)",
"state_before": "F : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.27241\nδ... | [
187,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_range_iff_mem_finset_range_of_mod_eq' | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.101231\nγ : Type ?u.101234\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns : Finset α\nt : Finset β\na✝ : α\nb c : β\ninst✝ : DecidableEq α\nf : ℕ → α\na : α\nn : ℕ\nhn : 0 < n\nh : ∀ (i : ℕ), f (i % n) = f i\n⊢ a ∈ Set.range f → a ∈ image (fun i => f i) (range n)\n... | [
562,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Algebra/Field/Basic.lean | Commute.inv_add_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17471\nK : Type ?u.17474\ninst✝ : DivisionSemiring α\na b c d : α\nhab : _root_.Commute a b\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a⁻¹ + b⁻¹ = (a + b) / (a * b)",
"tactic": "rw [inv_eq_one_div, inv_eq_one_div, hab.one_div_add_one_div ha hb]"
... | [
86,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/Topology/StoneCech.lean | ultrafilter_extend_extends | [
{
"state_after": "α : Type u\nγ : Type u_1\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space γ\nf : α → γ\nthis : TopologicalSpace α := ⊥\n⊢ Ultrafilter.extend f ∘ pure = f",
"state_before": "α : Type u\nγ : Type u_1\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space γ\nf : α → γ\n⊢ Ultrafilter.extend f ∘ pure = f",... | [
179,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/NhdsSet.lean | disjoint_nhdsSet_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8534\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ Disjoint (𝓝ˢ s) (𝓟 t) ↔ Disjoint s (closure t)",
"tactic": "rw [disjoint_comm, disjoint_principal_nhdsSet, disjoint_comm]"
}
] | [
68,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_empty | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.re_eq_self_of_le | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6835080\ninst✝ : IsROrC K\na : K\nh : ‖a‖ ≤ ↑re a\n⊢ ↑(↑re a) = a",
"tactic": "rw [← conj_eq_iff_re, conj_eq_iff_im, im_eq_zero_of_le h]"
}
] | [
746,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.zero_empty | [] | [
533,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_mul_negSucc' | [] | [
62,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
61,
15
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_eq_coe | [] | [
350,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
20
] |
Mathlib/Order/SymmDiff.lean | symmDiff_left_surjective | [] | [
526,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_map_eq_of_injective | [] | [
953,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Std/Logic.lean | Classical.not_not | [] | [
655,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
655,
16
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.embDomain_image | [
{
"state_after": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\nα : Type u_4\nβ : Type u_3\ns : SummableFamily Γ R α\nf : α ↪ β\na : α\nb : β\n⊢ toFun s (Classical.choose (_ : ↑f a ∈ Set.range ↑f)) = toFun s a",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrd... | [
1734,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1732,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Preconnected.subsingleton_connectedComponent | [] | [
2045,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2043,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.prod_mem | [] | [
354,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
11
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_of_mul_lt_of_one_le_left | [] | [
1054,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.ofLists_moveLeft | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.RightExactFunctor.forget_map | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.id_comp | [] | [
1273,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.left_dist_ne_zero_of_angle_eq_pi | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np1 p2 p3 : P\nh : ∠ p1 p2 p3 = π\nheq : dist p1 p2 = 0\n⊢ False",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst... | [
212,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/RingTheory/Adjoin/Tower.lean | Algebra.fg_trans' | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nS✝ : Type v\nA✝ : Type w\nB : Type u₁\nR : Type u_1\nS : Type u_2\nA : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring S\ninst✝⁴ : CommSemiring A\ninst✝³ : Algebra R S\ninst✝² : Algebra S A\ninst✝¹ : Algebra R A\ninst✝ : IsScalarTower R S A... | [
85,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_eq_lineMap_iff | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV1 : Type u_2\nP1 : Type u_3\nV2 : Type ?u.464024\nP2 : Type ?u.464027\nV3 : Type ?u.464030\nP3 : Type ?u.464033\nV4 : Type ?u.464036\nP4 : Type ?u.464039\ninst✝¹³ : Ring k\ninst✝¹² : AddCommGroup V1\ninst✝¹¹ : Module k V1\ninst✝¹⁰ : AffineSpace V1... | [
575,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean | CategoryTheory.SemiadditiveOfBinaryBiproducts.comp_add | [
{
"state_after": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasBinaryBiproducts C\nX Y Z : C\nf : X ⟶ Y\ng h : Y ⟶ Z\n⊢ (f ≫ biprod.lift g h) ≫ biprod.desc (𝟙 Z) (𝟙 Z) = biprod.lift (f ≫ g) (f ≫ h) ≫ biprod.desc (𝟙 Z) (𝟙 Z)",
"state_before": "C : Type u\ninst✝² : Category C\n... | [
139,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.leadingCoeff_div | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nhpq : degree q ≤ degree p\nhq : q = 0\n⊢ leadingCoeff (p / q) = leadingCoeff p / leadingCoeff q\n\ncase neg\nR : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np... | [
427,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/List/Join.lean | List.reverse_join | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.18531\n⊢ reverse (join []) = join (reverse (map reverse []))\n\ncase cons\nα : Type u_1\nβ : Type ?u.18531\nhead✝ : List α\ntail✝ : List (List α)\nih : reverse (join tail✝) = join (reverse (map reverse tail✝))\n⊢ reverse (join (head✝ :: tail✝)) = join (rever... | [
224,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_smul_measure | [
{
"state_after": "case inl\nα : Type u_2\nE : Type u_1\nF : Type ?u.1347471\n𝕜 : Type ?u.1347474\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\nins... | [
1515,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | Differentiable.const_mul | [] | [
493,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.nth_mk | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.Separable.of_dvd | [
{
"state_after": "case intro\nR : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\ng f' : R[X]\nhf : Separable (g * f')\n⊢ Separable g",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\nf g : R[X]\nhf : Separable f\nhfg : g ∣ f\n⊢ Separable g",
... | [
97,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Uniform.continuousAt_iff'_right | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.197144\ninst✝¹ : UniformSpace α\ninst✝ : TopologicalSpace β\nf : β → α\nb : β\n⊢ ContinuousAt f b ↔ Tendsto (fun x => (f b, f x)) (𝓝 b) (𝓤 α)",
"tactic": "rw [ContinuousAt, tendsto_nhds_right]... | [
1925,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1923,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffWithinAt.inter | [] | [
305,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.negIsPoly | [
{
"state_after": "p : ℕ\nR S : Type u\nσ : Type ?u.633934\nidx : Type ?u.633937\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : Fact (Nat.Prime p)\nR✝ : Type u_1\ninst✝ : CommRing R✝\nx✝ : 𝕎 R✝\n⊢ (-x✝).coeff = fun n => ↑(aeval x✝.coeff) ((fun n => ↑(rename Prod.snd) (wittNeg p n)) n)",
"state_before":... | [
483,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.prod_atBot | [
{
"state_after": "ι : Type ?u.286644\nι' : Type ?u.286647\nα : Type u_1\nβ : Type ?u.286653\nγ : Type u_2\ninst✝¹ : SemilatticeInf α\ninst✝ : SemilatticeInf γ\nf g : α → γ\nhf : Tendsto f atBot atBot\nhg : Tendsto g atBot atBot\n⊢ Tendsto (Prod.map f g) (atBot ×ˢ atBot) atBot",
"state_before": "ι : Type ?u.... | [
1458,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.even_add_odd | [
{
"state_after": "α : Type u_1\nβ : Type ?u.265508\nγ : Type ?u.265511\nδ : Type ?u.265514\ninst✝² : AddCommMonoid α\ninst✝¹ : TopologicalSpace α\nf✝ g : β → α\na b : α\ns : Finset β\ninst✝ : ContinuousAdd α\nf : ℕ → α\nhe : HasSum (fun k => f (2 * k)) a\nho : HasSum (fun k => f (2 * k + 1)) b\nthis : Injective... | [
377,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.left_nonuniformWitnesses_card | [
{
"state_after": "α : Type u_1\n𝕜 : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\na b : α\nh : ¬IsUniform G ε s t\n⊢ ↑(card s) * ε ≤\n ↑(card\n (Exists.choose\n (_ :\n ∃ s',\n s' ⊆ s ∧\n ... | [
137,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_units | [] | [
347,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_inter_cancel_right | [] | [
1027,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.add_mem | [] | [
265,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
11
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.coe_injective | [] | [
578,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Order/Basic.lean | Ne.le_iff_lt | [] | [
433,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Control/Functor/Multivariate.lean | MvFunctor.LiftR_RelLast_iff | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u_1\ninst✝¹ : MvFunctor F\ninst✝ : LawfulMvFunctor F\nα : TypeVec n\nβ : Type u\npp : β → Prop\nrr : β → β → Prop\nx y : F (α ::: β)\n⊢ (∃ u, (fun i t => (↑t).fst) <$$> u = x ∧ (fun i t => (↑t).snd) <$$> u = y) ↔\n ∃ u, (fun i t => (↑t).fst) <$$> u = x ∧ (f... | [
242,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_sub_pi | [] | [
810,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.congr_fun | [] | [
153,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
11
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_mul_ofReal | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nhr : 0 < r\nx : ℂ\nhx : x ≠ 0\n⊢ log (x * ↑r) = ↑(Real.log r) + log x",
"tactic": "rw [mul_comm, log_ofReal_mul hr hx, add_comm]"
}
] | [
89,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/PathConnected.lean | Path.map_trans | [
{
"state_after": "case a.h\nX : Type u_1\nY✝ : Type ?u.304721\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y✝\nx y z : X\nι : Type ?u.304736\nγ✝ γ : Path x y\nγ' : Path y z\nY : Type u_2\ninst✝ : TopologicalSpace Y\nf : X → Y\nh : Continuous f\nt : ↑I\n⊢ ↑(map (trans γ γ') h) t = ↑(trans (map γ h) (m... | [
443,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.of.zero_exact_aux | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁸ : Ring R\nι : Type v\ndec_ι : DecidableEq ι\ninst✝⁷ : Preorder ι\nG : ι → Type w\ninst✝⁶ : (i : ι) → AddCommGroup (G i)\ninst✝⁵ : (i : ι) → Module R (G i)\nf : (i j : ι) → i ≤ j → G i →ₗ[R] G j\nP : Type u₁\ninst✝⁴ : AddCommGroup P\ninst✝³ : M... | [
252,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.re_add_im | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (↑z.re + ↑z.im * I).re = z.re ∧ (↑z.re + ↑z.im * I).im = z.im",
"tactic": "simp [ofReal']"
}
] | [
335,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_Prop | [] | [
750,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Set.algebraMap_mem_center | [
{
"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 : Subalgebra R A\nr : R\n⊢ ↑(algebraMap R A) r ∈ Set.center A",
"tactic": "simp [Algebra.commutes, Set.mem_cen... | [
1337,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.decompose_one | [] | [
86,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
src/lean/Init/Data/Array/Mem.lean | Array.sizeOf_get | [
{
"state_after": "case mk\nα : Type u_1\ninst✝ : SizeOf α\ndata✝ : List α\ni : Fin (size { data := data✝ })\n⊢ sizeOf (get { data := data✝ } i) < sizeOf { data := data✝ }",
"state_before": "α : Type u_1\ninst✝ : SizeOf α\nas : Array α\ni : Fin (size as)\n⊢ sizeOf (get as i) < sizeOf as",
"tactic": "case... | [
48,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
44,
9
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | parallelogram_law | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1814317\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ inner x x + inner x y + inner y x + inner y y + (inner x x - inn... | [
705,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.prod | [] | [
112,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.inner_left_of_mem_orthogonal | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.23535\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nK : Submodule 𝕜 E\nu v : E\nhu : u ∈ K\nhv : v ∈ Kᗮ\n⊢ inner u v = 0",
"state_before": "𝕜 : T... | [
75,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_sub_pi | [] | [
1307,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1306,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.181246\nγ : Type ?u.181249\ninst✝ : DecidableEq α\ns s₁✝ s₂✝ t t₁ t₂ u v : Finset α\na b : α\ns₁ s₂ : Finset α\nx✝ : α\n⊢ x✝ ∈ s₁ ∩ s₂ ↔ x✝ ∈ s₂ ∩ s₁",
"tactic": "simp only [mem_inter, and_comm]"
}
] | [
1612,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1611,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_comp_unop | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/List/Basic.lean | List.subset_singleton_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.18245\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nL : List α\n⊢ L ⊆ [a] ↔ ∃ n, L = replicate n a",
"tactic": "simp only [eq_replicate, subset_def, mem_singleton, exists_eq_left']"
}
] | [
453,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.add_left_cancel | [
{
"state_after": "m n a b c d : ℕ\nh₁ : ↑n ∣ ↑b - ↑a\nh₂ : ↑n ∣ ↑b + ↑d - (↑a + ↑c)\n⊢ ↑n ∣ ↑d - ↑c",
"state_before": "m n a b c d : ℕ\nh₁ : a ≡ b [MOD n]\nh₂ : a + c ≡ b + d [MOD n]\n⊢ c ≡ d [MOD n]",
"tactic": "simp only [modEq_iff_dvd, Int.ofNat_add] at *"
},
{
"state_after": "m n a b c d : ℕ... | [
159,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
11
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodCongrLeft_apply | [] | [
709,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.coe_id | [] | [
291,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_eq_right_inv | [] | [
454,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.18308\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSp... | [
108,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_zero | [
{
"state_after": "⊢ prod 0 = 1",
"state_before": "⊢ prod 0 = 1",
"tactic": "dsimp [Prod]"
},
{
"state_after": "no goals",
"state_before": "⊢ prod 0 = 1",
"tactic": "exact Multiset.prod_zero"
}
] | [
220,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.singularPart_totalVariation | [
{
"state_after": "α : Type u_1\nβ : Type ?u.301151\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns : SignedMeasure α\nμ : Measure α\nthis :\n toJordanDecomposition (singularPart s μ) =\n JordanDecomposition.mk (Measure.singularPart (toJordanDecomposition s).posPart μ)\n (Measure.singularPart (toJordanDecom... | [
878,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_add_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ sin (x + π / 2) = cos x",
"tactic": "simp [sin_add]"
}
] | [
445,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.continuousWithinAt_symm | [] | [
244,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.true_xor | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ xor true b = !b",
"tactic": "cases b <;> simp"
}
] | [
60,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Set/Image.lean | Set.Subsingleton.image | [] | [
1219,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.size_eq | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Sigma/Order.lean | Sigma.Lex.lt_def | [] | [
152,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Subgroup.rank_closure_finset_le_card | [
{
"state_after": "M : Type ?u.114803\nN : Type ?u.114806\ninst✝³ : Monoid M\ninst✝² : AddMonoid N\nG : Type u_1\nH : Type ?u.114818\ninst✝¹ : Group G\ninst✝ : AddGroup H\ns : Finset G\nt : Finset { x // x ∈ closure ↑s } := Finset.preimage s Subtype.val (_ : Set.InjOn (fun a => ↑a) (Subtype.val ⁻¹' ↑s))\n⊢ Group... | [
451,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.disjoint | [] | [
896,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.map_div | [] | [
710,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
11
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.