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 |
|---|---|---|---|---|---|---|
Std/Data/Rat/Lemmas.lean | Rat.normalize_add_normalize | [
{
"state_after": "case mk'\nn₁ n₂ : Int\nd₁ d₂ : Nat\nz₁ : d₁ ≠ 0\nz₂ : d₂ ≠ 0\nnum✝ : Int\nden✝ : Nat\nden_nz✝ : den✝ ≠ 0\nreduced✝ : Nat.coprime (Int.natAbs num✝) den✝\ne₁ : normalize n₁ d₁ = mk' num✝ den✝\n⊢ mk' num✝ den✝ + normalize n₂ d₂ = normalize (n₁ * ↑d₂ + n₂ * ↑d₁) (d₁ * d₂)",
"state_before": "n₁... | [
193,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
186,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_one_eq_two | [
{
"state_after": "case zero\nm : ℕ\ninst✝ : NeZero zero\n⊢ succ 1 = 2\n\ncase succ\nm n✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\n⊢ succ 1 = 2",
"state_before": "n m : ℕ\ninst✝ : NeZero n\n⊢ succ 1 = 2",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case zero\nm : ℕ\ninst✝ :... | [
927,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_subsingleton | [
{
"state_after": "case a.h\nm : Type u\nn : Type v\nα : Type w\ninst✝⁵ : DecidableEq n\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq m\ninst✝² : Fintype m\ninst✝¹ : CommRing α\ninst✝ : Subsingleton n\nA : Matrix n n α\ni j : n\n⊢ adjugate A i j = OfNat.ofNat 1 i j",
"state_before": "m : Type u\nn : Type v\nα : ... | [
321,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.zero_apply | [] | [
153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.sup_support_add_le | [] | [
53,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_toPrenex | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.229555\nP : Type ?u.229558\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs : Fin l → M\n... | [
568,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.transferNatTransSelf_comm | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\nD : Type u₂\ninst✝¹ : Category C\ninst✝ : Category D\nL₁ L₂ L₃ : C ⥤ D\nR₁ R₂ R₃ : D ⥤ C\nadj₁ : L₁ ⊣ R₁\nadj₂ : L₂ ⊣ R₂\nadj₃ : L₃ ⊣ R₃\nf : L₂ ⟶ L₁\ng : L₁ ⟶ L₂\ngf : g ≫ f = 𝟙 L₁\n⊢ ↑(transferNatTransSelf adj₁ adj₂) f ≫ ↑(transferNatTransSelf ad... | [
229,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.ne_top_iff_dom | [
{
"state_after": "no goals",
"state_before": "x : PartENat\n⊢ x ≠ ⊤ ↔ x.Dom",
"tactic": "classical exact not_iff_comm.1 Part.eq_none_iff'.symm"
},
{
"state_after": "no goals",
"state_before": "x : PartENat\n⊢ x ≠ ⊤ ↔ x.Dom",
"tactic": "exact not_iff_comm.1 Part.eq_none_iff'.symm"
}
] | [
370,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Int.natAbs_le_self_sq | [
{
"state_after": "α : Type ?u.316248\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\na : ℤ\n⊢ ↑(natAbs a) ≤ ↑(natAbs a) * ↑(natAbs a)",
"state_before": "α : Type ?u.316248\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\... | [
782,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.image_mulSingle_Ioo_left | [] | [
249,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_sup | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.95383\nK : Type ?u.95386\nM : Type u_1\nM₂ : Type ?u.95392\nV : Type ?u.95395\nS : Type ?u.95398\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ :... | [
359,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Topology/Connected.lean | isPreconnected_of_forall | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nι : Type ?u.1489\nπ : ι → Type ?u.1494\ninst✝ : TopologicalSpace α\ns✝ t u✝ v✝ s : Set α\nx : α\nH : ∀ (y : α), y ∈ s → ∃ t, t ⊆ s ∧ x ∈ t ∧ y ∈ t ∧ IsPreconnected t\nu v : Set α\nhu : IsOpen u\nhv : IsOpen v\nhs : s ⊆ u ∪ v\nz : α\nzs : z ... | [
117,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.lt_top | [] | [
114,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.other_spec | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.34981\nγ : Type ?u.34984\na : α\nz : Sym2 α\nh : a ∈ z\n⊢ Quotient.mk (Rel.setoid α) (a, Mem.other h) = z",
"tactic": "erw [← Classical.choose_spec h]"
}
] | [
366,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.directed_on_iUnion | [
{
"state_after": "α : Type u_1\nβ : Type ?u.72615\nγ : Type ?u.72618\nι : Sort u_2\nι' : Sort ?u.72624\nι₂ : Sort ?u.72627\nκ : ι → Sort ?u.72632\nκ₁ : ι → Sort ?u.72637\nκ₂ : ι → Sort ?u.72642\nκ' : ι' → Sort ?u.72647\nr : α → α → Prop\nf : ι → Set α\nhd : Directed (fun x x_1 => x ⊆ x_1) f\nh : ∀ (x : ι), Dire... | [
582,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.log_pow_int_eq_self | [] | [
510,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.wellFoundedOn_insert | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.108524\nα : Type u_1\nβ : Type ?u.108530\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\ns : Set α\na : α\n⊢ WellFoundedOn (insert a s) r ↔ WellFoundedOn s r",
"tactic": "simp only [← singleton_union, wellFoundedOn_union, wellFoundedOn_singleton, t... | [
508,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/CategoryTheory/DiscreteCategory.lean | CategoryTheory.Discrete.eq_of_hom | [] | [
136,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_sub_sq_real | [] | [
1074,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1073,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.induction_of_closure_eq_top_right | [
{
"state_after": "M : Type u_1\nA : Type ?u.92434\nB : Type ?u.92437\ninst✝ : Monoid M\ns : Set M\np : M → Prop\nhs : closure s = ⊤\nx : M\nH1 : p 1\nHmul : ∀ (x y : M), y ∈ s → p x → p (x * y)\n⊢ x ∈ ⊤",
"state_before": "M : Type u_1\nA : Type ?u.92434\nB : Type ?u.92437\ninst✝ : Monoid M\ns : Set M\np : M... | [
422,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.refl_symm | [] | [
864,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_inv | [] | [
270,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | DifferentiableOn.star | [] | [
82,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_le_one_of_subsingleton | [] | [
556,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integrable_of_integral_norm_bounded | [
{
"state_after": "α : Type u_2\nι : Type u_1\nE : Type u_3\ninst✝³ : MeasurableSpace α\nμ : Measure α\nl : Filter ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NeBot l\ninst✝ : IsCountablyGenerated l\nφ : ι → Set α\nhφ : AECover μ l φ\nf : α → E\nI : ℝ\nhfi : ∀ (i : ι), IntegrableOn f (φ i)\nhbounded : ∀ᶠ (i : ι) ... | [
454,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sSameSide_vadd_right_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.138969\nP : Type u_3\nP' : Type ?u.138975\ninst✝⁶ : StrictOrderedCommRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns... | [
300,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.eq_bot_or_top | [
{
"state_after": "ι : Type ?u.28720\nα✝ : Type ?u.28723\nβ : Type ?u.28726\nγ : Type ?u.28729\ninst✝² : TopologicalSpace α✝\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nα : Type u_1\nU : Opens α\n⊢ U = ⊥ ∨ U = ⊤",
"state_before": "ι : Type ?u.28720\nα✝ : Type ?u.28723\nβ : Type ?u.28726\nγ : Ty... | [
282,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_comp_le | [] | [
987,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.mul_inv_cancel | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na b : G\nh : Commute a b\n⊢ a * b * a⁻¹ = b",
"tactic": "rw [h.eq, mul_inv_cancel_right]"
}
] | [
392,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
11
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_comp | [] | [
683,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/GroupTheory/Solvable.lean | isSolvable_of_comm | [
{
"state_after": "G✝ : Type ?u.40798\nG' : Type ?u.40801\ninst✝¹ : Group G✝\ninst✝ : Group G'\nf : G✝ →* G'\nG : Type u_1\nhG : Group G\nh : ∀ (a b : G), a * b = b * a\nhG' : CommGroup G := CommGroup.mk h\n⊢ IsSolvable G",
"state_before": "G✝ : Type ?u.40798\nG' : Type ?u.40801\ninst✝¹ : Group G✝\ninst✝ : G... | [
127,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.thin_diagram_of_surjective | [
{
"state_after": "no goals",
"state_before": "J : Type u\ninst✝¹ : Category J\nF : J ⥤ Type v\ni✝ j✝ k✝ : J\ns : Set (F.obj i✝)\ninst✝ : IsCofilteredOrEmpty J\nFsur : ∀ ⦃i j : J⦄ (f : i ⟶ j), Function.Surjective (F.map f)\ni j : J\nf g : i ⟶ j\nk : J\nφ : k ⟶ i\nhφ : φ ≫ f = φ ≫ g\n⊢ (fun g => g ∘ F.map φ) ... | [
323,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_finset_image | [] | [
2064,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2062,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | idRestrGroupoid_mem | [] | [
432,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.union_right | [] | [
122,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.ext_fourfold | [
{
"state_after": "case H.H.H.h.h.h.h\nR : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.721821\ninst✝¹³ : Monoid R'\nR'' : Type ?u.721827\ninst✝¹² : Semiring R''\nM : Type u_5\nN : Type u_4\nP : Type u_3\nQ : Type u_2\nS : Type u_6\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoid... | [
603,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_ne_zero_iff | [] | [
1295,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Std/Data/List/Lemmas.lean | List.mem_cons | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na b : α✝\nl : List α✝\nh : a ∈ b :: l\n⊢ a = b ∨ a ∈ l",
"tactic": "cases h <;> simp [Membership.mem, *]"
},
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na b : α✝\nl : List α✝\n⊢ a ∈ a :: l",
"tactic": "construc... | [
64,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
62,
9
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coeSubmodule_le_coeSubmodule | [] | [
362,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Topology/Order/Basic.lean | TFAE_mem_nhdsWithin_Ici | [
{
"state_after": "case tfae_1_iff_2\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na b : α\nhab : a < b\ns : Set α\n⊢ s ∈ 𝓝[Ici a] a ↔ s ∈ 𝓝[Icc a b] a\n\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α... | [
1753,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1734,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.pos_eq_endPos | [
{
"state_after": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ utf8Len l = utf8Len l + utf8Len r ↔ r = []",
"state_before": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ it.i = endPos it.s ↔ r = []",
"tactic": "simp [h.pos, h.toString, Pos.ext_iff]"
},
{
"state_after": "no go... | [
543,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
541,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.finrank_finsupp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nN : Type w\ninst✝¹⁰ : Ring R\ninst✝⁹ : StrongRankCondition R\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\ninst✝⁶ : Module.Free R M\ninst✝⁵ : Module.Finite R M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module R N\ninst✝² : Module.Free R N\ninst... | [
99,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.comp' | [] | [
880,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.map | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nx y z : R\nH : IsCoprime x y\nS : Type v\ninst✝ : CommSemiring S\nf : R →+* S\na b : R\nh : a * x + b * y = 1\n⊢ ↑f a * ↑f x + ↑f b * ↑f y = 1",
"tactic": "rw [← f.map_mul, ← f.map_mul, ← f.map_add, h, f.map_one]"
}
] | [
179,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.24923\nE : Type u_2\nF : Type u_3\nG : Type ?u.24932\nE' : Type ?u.24935\nF' : Type ?u.24938\nG' : Type ?u.24941\nE'' : Type ?u.24944\nF'' : Type ?u.24947\nG'' : Type ?u.24950\nR : Type ?u.24953\nR' : Type ?u.24956\n𝕜 : Type ?u.24959\n... | [
159,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolAlg_toBoolAlg | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.smul_inv | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type ?u.2011824\nk : Type u_2\ninst✝ : Field k\nr : k\nφ : MvPowerSeries σ k\n⊢ (r • φ)⁻¹ = r⁻¹ • φ⁻¹",
"tactic": "simp [smul_eq_C_mul, mul_comm]"
}
] | [
1046,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.int_cast_eq_int_cast_iff | [] | [
459,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_mul_right_iff' | [] | [
1538,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1536,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.neg_imI | [] | [
246,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
9
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.edist_le | [] | [
115,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | RingHom.map_det | [
{
"state_after": "no goals",
"state_before": "m : Type ?u.1465983\nn : Type u_1\ninst✝⁵ : DecidableEq n\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq m\ninst✝² : Fintype m\nR : Type v\ninst✝¹ : CommRing R\nS : Type w\ninst✝ : CommRing S\nf : R →+* S\nM : Matrix n n R\n⊢ ↑f (det M) = det (↑(RingHom.mapMatrix f) ... | [
332,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_sSup_of_directedOn | [
{
"state_after": "M : Type u_1\nA : Type ?u.37107\nB : Type ?u.37110\ninst✝ : MulOneClass M\nS : Set (Submonoid M)\nSne : Set.Nonempty S\nhS : DirectedOn (fun x x_1 => x ≤ x_1) S\nx : M\nthis : Nonempty ↑S\n⊢ x ∈ sSup S ↔ ∃ s, s ∈ S ∧ x ∈ s",
"state_before": "M : Type u_1\nA : Type ?u.37107\nB : Type ?u.371... | [
225,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_union_closure_left | [] | [
507,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_le | [] | [
68,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | LinearEquiv.isAssociatedPrime_iff | [] | [
75,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/Complex/RemovableSingularity.lean | Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAt | [
{
"state_after": "case intro.intro\nE : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nc : ℂ\nhd : ∀ᶠ (z : ℂ) in 𝓝[{c}ᶜ] c, DifferentiableAt ℂ f z\nhc : ContinuousAt f c\nR : ℝ\nhR0 : 0 < R\nhRs : closedBall c R ∩ {c}ᶜ ⊆ {x | (fun z => DifferentiableAt ℂ f ... | [
48,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/Algebra/Pi.lean | AlgEquiv.piCongrRight_refl | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_const | [] | [
1131,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
] |
Mathlib/FieldTheory/Laurent.lean | RatFunc.laurentAux_ofFractionRing_mk | [] | [
66,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_neg | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.inv_liminf | [] | [
530,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subsingleton.strictMono | [] | [
499,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_sub_int_mul_two_pi | [] | [
1252,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_cons_zero | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\na : α\nv : Vector α n\n⊢ get (a ::ᵥ v) 0 = a",
"tactic": "simp [get_zero]"
}
] | [
267,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Isometry.lean | QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate' | [
{
"state_after": "case intro\nι : Type ?u.195680\nR : Type ?u.195683\nK : Type u_1\nM : Type ?u.195689\nM₁ : Type ?u.195692\nM₂ : Type ?u.195695\nM₃ : Type ?u.195698\nV : Type u_2\ninst✝¹⁴ : Semiring R\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : AddCommMonoid M₁\ninst✝¹¹ : AddCommMonoid M₂\ninst✝¹⁰ : AddCommMonoid M₃... | [
171,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_inclusion | [] | [
571,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.mrange_eq_iSup | [
{
"state_after": "ι : Type u_3\nM : ι → Type u_2\ninst✝² : (i : ι) → Monoid (M i)\nN✝ : Type ?u.257223\ninst✝¹ : Monoid N✝\nN : Type u_1\ninst✝ : Monoid N\nf : (i : ι) → M i →* N\n⊢ (⨆ (i : ι), MonoidHom.mrange (f i)) ≤ MonoidHom.mrange (↑lift f)",
"state_before": "ι : Type u_3\nM : ι → Type u_2\ninst✝² : (... | [
211,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Quot.lean | Quotient.eq'' | [] | [
781,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
11
] |
Mathlib/Data/List/Count.lean | List.countp_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl✝ : List α\np q : α → Bool\na : α\nl : List α\n⊢ countp p (a :: l) = countp p l + if p a = true then 1 else 0",
"tactic": "by_cases h : p a <;> simp [h]"
}
] | [
64,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_refl | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_compTendsto' | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.zero_shiftl | [] | [
47,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.continuousAt_of_dominated_interval | [] | [
1099,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_empty | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.6671\nδ : Type ?u.6674\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx✝ : α × β\n⊢ x✝ ∈ s ×ˢ ∅ ↔ x✝ ∈ ∅",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.6671\nδ : Type ?u.6674\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\n⊢ s ... | [
113,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.qp_eq | [
{
"state_after": "case pos\nu : XgcdType\nhr : r u = 0\nhq : q u = 0\n⊢ q u = qp u + 1\n\ncase neg\nu : XgcdType\nhr : r u = 0\nhq : ¬q u = 0\n⊢ q u = qp u + 1",
"state_before": "u : XgcdType\nhr : r u = 0\n⊢ q u = qp u + 1",
"tactic": "by_cases hq : u.q = 0"
},
{
"state_after": "case pos\nu : X... | [
249,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_empty | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.differentiableOn | [] | [
285,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.fromBlocks | [
{
"state_after": "α : Type u_2\nβ : Type ?u.7912\nn : Type u_3\nm : Type u_1\nR : Type ?u.7921\nA : Matrix m m α\nB : Matrix m n α\nC : Matrix n m α\nD : Matrix n n α\nhA : IsSymm A\nhBC : Bᵀ = C\nhD : IsSymm D\nhCB : Cᵀ = B\n⊢ IsSymm (Matrix.fromBlocks A B C D)",
"state_before": "α : Type u_2\nβ : Type ?u.... | [
142,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | inducing_pullbackTotalSpaceEmbedding | [
{
"state_after": "case induced\nB : Type u\nF : Type v\nE : B → Type w₁\nB' : Type w₂\nf✝ : B' → B\ninst✝¹ : TopologicalSpace B'\ninst✝ : TopologicalSpace (TotalSpace E)\nf : B' → B\n⊢ Pullback.TotalSpace.topologicalSpace E f = induced (pullbackTotalSpaceEmbedding f) instTopologicalSpaceProd",
"state_before... | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Injective.injective_iff_preservesEpimorphisms_yoneda_obj | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nJ : C\n⊢ Functor.PreservesEpimorphisms (coyoneda.obj J.op.op) ↔ Functor.PreservesEpimorphisms (yoneda.obj J)",
"state_before": "C : Type u₁\ninst✝ : Category C\nJ : C\n⊢ Injective J ↔ Functor.PreservesEpimorphisms (yoneda.obj J)",
"tactic": "rw [injecti... | [
195,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Iic_iInf₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.121800\nγ : Type ?u.121803\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : CompleteLattice α\nf : (i : ι) → κ i → α\n⊢ Iic (⨅ (i : ι) (j : κ i), f i j) = ⨅ (i : ι) (j : κ i), Iic (f i j)",
"tactic": "simp_rw [Iic_iInf]"
}
] | [
1247,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_le_right | [] | [
150,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isWf_univ_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.36350\nα : Type u_1\nβ : Type ?u.36356\ninst✝ : LT α\ns t : Set α\n⊢ IsWf univ ↔ WellFounded fun x x_1 => x < x_1",
"tactic": "simp [IsWf, wellFoundedOn_iff]"
}
] | [
196,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.iff_forall_not_isBadSeq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.134113\nα : Type u_1\nβ : Type ?u.134119\nr✝ r : α → α → Prop\ns : Set α\nf : ℕ → α\n⊢ ((∀ (n : ℕ), f n ∈ s) → ∃ m n, m < n ∧ r (f m) (f n)) ↔ ¬IsBadSeq r s f",
"tactic": "simp [IsBadSeq]"
}
] | [
684,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.succ_le_succ_sqrt | [] | [
191,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.zero_lt_sub_of_lt | [
{
"state_after": "no goals",
"state_before": "i a : Nat\nh : i < a\n⊢ 0 < a - i",
"tactic": "induction a with\n| zero => contradiction\n| succ a ih =>\n match Nat.eq_or_lt_of_le h with\n | Or.inl h => injection h with h; subst h; rw [←Nat.add_one, Nat.add_sub_self_left]; decide\n | Or.inr h =>\n h... | [
555,
62
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
547,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.mapsTo_fixedPoints_comp | [] | [
172,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.eq_set_map_one_map_mul | [
{
"state_after": "case h\n𝕜 : Type u_1\nA : Type u_2\ninst✝⁸ : CommRing 𝕜\ninst✝⁷ : NoZeroDivisors 𝕜\ninst✝⁶ : TopologicalSpace 𝕜\ninst✝⁵ : ContinuousAdd 𝕜\ninst✝⁴ : ContinuousConstSMul 𝕜 𝕜\ninst✝³ : TopologicalSpace A\ninst✝² : Semiring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : Nontrivial 𝕜\nφ : WeakDual 𝕜 A\... | [
176,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.tensor_right_unitality | [
{
"state_after": "C : Type u₁\ninst✝⁸ : Category C\ninst✝⁷ : MonoidalCategory C\ninst✝⁶ : BraidedCategory C\nD : Type u₂\ninst✝⁵ : Category D\ninst✝⁴ : MonoidalCategory D\ninst✝³ : BraidedCategory D\nE : Type u₃\ninst✝² : Category E\ninst✝¹ : MonoidalCategory E\ninst✝ : BraidedCategory E\nX₁ X₂ : C\n⊢ (ρ_ (X₁ ⊗... | [
449,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Data/List/Zip.lean | List.map_prod_left_eq_zip | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type ?u.87662\nδ : Type ?u.87665\nε : Type ?u.87668\nl : List α\nf : α → β\n⊢ zip (map (fun x => x) l) (map (fun x => f x) l) = zip l (map f l)",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.87662\nδ : Type ?u.87665\nε : Type ?u.87668\nl : List α\nf ... | [
260,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_map_equiv | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nE : Type u_3\nF : Type ?u.1520469\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\nf✝ g : α → E\ns✝ t : Set α\nμ✝ ν : Measure α\ninst✝ : MeasurableSpace β\ne : α ≃ᵐ β\nf : β → E\nμ : Measure α\ns : Set β\n⊢ IntegrableOn f s... | [
245,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePushout.head_desc | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type u_1\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → B ⟶ objs j\ninst✝ : HasWidePushout B objs arrows\nX : D\nf : B ⟶ X\nfs : (j : J) → objs j ⟶ X\nw : ∀ (j : J), arrows j ≫ fs j = f\n⊢ head arro... | [
428,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_singleton | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.97519\nγ : Type ?u.97522\ns t : Set α\na : α\ninst✝ : Fintype ↑{a}\na✝ : α\n⊢ a✝ ∈ toFinset {a} ↔ a✝ ∈ {a}",
"state_before": "α : Type u_1\nβ : Type ?u.97519\nγ : Type ?u.97522\ns t : Set α\na : α\ninst✝ : Fintype ↑{a}\n⊢ toFinset {a} = {a}",
"tactic":... | [
783,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.Hσ_eq_zero | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ HomologicalComplex.Hom.f (nullHomotopicMap' (hσ' q)) 0 = 0",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ HomologicalComplex.Hom.f (Hσ q... | [
156,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.one_rpow | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ 1 ^ x = 1",
"tactic": "simp [rpow_def]"
}
] | [
133,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_subset_iff | [] | [
306,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.trans_iterate_Ico | [
{
"state_after": "ι : Type ?u.2084269\n𝕜 : Type ?u.2084272\nE : Type u_1\nF : Type ?u.2084278\nA : Type ?u.2084281\ninst✝ : NormedAddCommGroup E\nf : ℝ → E\na✝ b c d : ℝ\nμ ν : MeasureTheory.Measure ℝ\na : ℕ → ℝ\nm n : ℕ\nhmn : m ≤ n\n⊢ (∀ (k : ℕ), k ∈ Ico m n → IntervalIntegrable f μ (a k) (a (k + 1))) → Inte... | [
164,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Sign.lean | SignType.not_one_lt | [] | [
221,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.comp_antitoneOn | [] | [
662,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.