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/Nat/Cast/Basic.lean | Nat.coe_castRingHom | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.differentiableAt_cos | [] | [
619,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lmapDomain_disjoint_ker | [
{
"state_after": "α : Type u_1\nM : Type u_3\nN : Type ?u.251779\nP : Type ?u.251782\nR : Type u_4\nS : Type ?u.251788\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nα' : Type ... | [
511,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lie_eq_bot_iff | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
152,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mem_one | [] | [
510,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Measure.integral_comp_inv_mul_left | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.90285\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Norme... | [
118,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_finset' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.369968\nγ : Type ?u.369971\nδ : Type ?u.369974\nι : Type ?u.369977\nR : Type ?u.369980\nR' : Type ?u.369983\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Se... | [
2209,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2204,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.eq_zero_of_eval_eq_zero | [
{
"state_after": "no goals",
"state_before": "σ K : Type u\ninst✝² : Fintype K\ninst✝¹ : Field K\ninst✝ : Finite σ\np : MvPolynomial σ K\nh : ∀ (v : σ → K), ↑(eval v) p = 0\nhp : p ∈ restrictDegree σ K (Fintype.card K - 1)\np' : R σ K := { val := p, property := hp }\nthis : p' ∈ ker (evalᵢ σ K)\n⊢ p' = 0",
... | [
258,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsInitial.hasInitial | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX : C\nh : IsInitial X\nF : Discrete PEmpty ⥤ C\n⊢ (X_1 : Discrete PEmpty) → F.obj X_1 ⟶ ((Functor.const (Discrete PEmpty)).obj X).obj X_1",
"tactic": "aesop_cat"
},
{
"state_after": "no goals",
"state_before": "C... | [
341,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_right_eq_self_iff | [
{
"state_after": "no goals",
"state_before": "m n k a b : ℕ\nha : 0 < a\nthis : a * b = a * 1 ↔ b = 1\n⊢ a * b = a ↔ b = 1",
"tactic": "rwa [mul_one] at this"
}
] | [
355,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_le_iff_left | [] | [
618,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.le_minFac' | [
{
"state_after": "m p : ℕ\npp : 1 < p\nh : 1 = 1 ∨ m ≤ minFac 1\nd : p ∣ 1\n⊢ m ≤ p",
"state_before": "m n : ℕ\nh : n = 1 ∨ m ≤ minFac n\np : ℕ\npp : 1 < p\nd : p ∣ n\n⊢ n = 1 → m ≤ p",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_before": "m p : ℕ\npp : 1 < p\nh : 1 = 1 ∨ m... | [
362,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.val_eq_iff_norm_eq | [
{
"state_after": "case h₀\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : ¬f ≈ 0\nhg : ¬g ≈ 0\n⊢ 0 < ↑p\n\ncase h₁\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : ¬f ≈ 0\nhg : ¬g ≈ 0\n⊢ ↑p ≠ 1",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : ¬f ≈ 0\nhg : ¬g ... | [
240,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_node3L | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ dual (node3L l x m y r) = node3R (dual r) y (dual m) x (dual l)",
"tactic": "simp [node3L, node3R, dual_node', add_comm]"
}
] | [
317,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.ennreal_tsum | [
{
"state_after": "α : Type u_2\nβ : Type ?u.2919204\nγ : Type ?u.2919207\nγ₂ : Type ?u.2919210\nδ : Type ?u.2919213\nι✝ : Sort y\ns t u : Set α\ninst✝¹ : MeasurableSpace α\nι : Type u_1\ninst✝ : Countable ι\nf : ι → α → ℝ≥0∞\nh : ∀ (i : ι), Measurable (f i)\n⊢ Measurable fun x => ⨆ (s : Finset ι), ∑ i in s, f i... | [
1932,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1928,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_and_distrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.169644\nι : Sort x\nf : Filter α\np : α → Prop\nq : Prop\n⊢ (∃ᶠ (x : α) in f, p x ∧ q) ↔ (∃ᶠ (x : α) in f, p x) ∧ q",
"tactic": "simp only [@and_comm _ q, frequently_and_distrib_left]"
}
] | [
1382,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1380,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.algebraMap_eq_one_iff | [] | [
433,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.sInter_singleton | [
{
"state_after": "no goals",
"state_before": "x y : ZFSet\n⊢ y ∈ ⋂₀ {x} ↔ y ∈ x",
"tactic": "simp_rw [mem_sInter (singleton_nonempty x), mem_singleton, forall_eq]"
}
] | [
1098,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_preimage_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.226621\nι : Sort ?u.226624\nι' : Sort ?u.226627\nι₂ : Sort ?u.226630\nκ : ι → Sort ?u.226635\nκ₁ : ι → Sort ?u.226640\nκ₂ : ι → Sort ?u.226645\nκ' : ι' → Sort ?u.226650\nf : α → β\ns : Set β\n⊢ (⋃ (y : β) (_ : y ∈ s), f ⁻¹... | [
1747,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1746,
1
] |
Mathlib/Algebra/Quandle.lean | Quandle.fix_inv | [
{
"state_after": "Q : Type u_1\ninst✝ : Quandle Q\nx : Q\n⊢ x ◃ x ◃⁻¹ x = x ◃ x",
"state_before": "Q : Type u_1\ninst✝ : Quandle Q\nx : Q\n⊢ x ◃⁻¹ x = x",
"tactic": "rw [← left_cancel x]"
},
{
"state_after": "no goals",
"state_before": "Q : Type u_1\ninst✝ : Quandle Q\nx : Q\n⊢ x ◃ x ◃⁻¹ x =... | [
420,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Logic/Basic.lean | xor_iff_not_iff' | [
{
"state_after": "no goals",
"state_before": "a b : Prop\n⊢ Xor' a b ↔ (¬a ↔ b)",
"tactic": "simp only [← @xor_not_left _ b, not_not]"
}
] | [
481,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.alternatingFaceMapComplex_map_f | [] | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.ext | [] | [
118,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_le_left | [] | [
478,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Topology/Basic.lean | interior_sInter_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\nS : Set (Set α)\n⊢ interior (⋂₀ S) = interior (⋂ (s : Set α) (_ : s ∈ S), s)",
"tactic": "rw [sInter_eq_biInter]"
}
] | [
401,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.coe_iSup_eq | [
{
"state_after": "R : Type ?u.772186\nR' : Type ?u.772189\n𝕜 : Type u_2\n𝕜₂ : Type ?u.772195\n𝕜₃ : Type ?u.772198\n𝕝 : Type ?u.772201\nE : Type u_3\nE₂ : Type ?u.772207\nE₃ : Type ?u.772210\nF : Type ?u.772213\nG : Type ?u.772216\nι✝ : Type ?u.772219\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ ... | [
591,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_sInf | [] | [
938,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Data/List/Basic.lean | List.map_join | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.133368\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β\nL : List (List α)\n⊢ map f (join L) = join (map (map f) L)",
"tactic": "induction L <;> [rfl; simp only [*, join, map, map_append]]"
}
] | [
1808,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1807,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.inv_whiskerLeft | [
{
"state_after": "case hom_inv_id\nB : Type u\ninst : Bicategory B\na b c d e : B\nf : a ⟶ b\ng h : b ⟶ c\nη : g ⟶ h\ninst_1 : IsIso η\n⊢ f ◁ η ≫ f ◁ inv η = 𝟙 (f ≫ g)",
"state_before": "B : Type u\ninst✝¹ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng h : b ⟶ c\nη : g ⟶ h\ninst✝ : IsIso η\n⊢ inv (f ◁ η) = f ... | [
234,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.isColimit_exists_rep | [
{
"state_after": "case intro\nC : Type u\ninst✝³ : Category C\ninst✝² : ConcreteCategory C\nJ : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ C\ninst✝ : PreservesColimit F (forget C)\nD : Cocone F\nhD : IsColimit D\na : (j : J) × (forget C).obj (F.obj j)\n⊢ ∃ j y, (forget C).map (D.ι.app j) y = (fun a => (forget C)... | [
205,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf₂_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_5\nβ : Type ?u.96031\nβ₂ : Type ?u.96034\nγ : Type ?u.96037\nι : Sort ?u.96040\nι' : Sort ?u.96043\nκ : ι → Sort ?u.96048\nκ' : ι' → Sort ?u.96053\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\nι₁ : Sort u_1\nι₂ : Sort u_2\nκ₁ : ι₁ → Sort u_3\... | [
1153,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Subalgebra.finiteDimensional_sup | [
{
"state_after": "K : Type u_1\nL : Type u_2\ninst✝⁴ : Field K\ninst✝³ : CommRing L\ninst✝² : Algebra K L\nE1 E2 : Subalgebra K L\ninst✝¹ : FiniteDimensional K { x // x ∈ E1 }\ninst✝ : FiniteDimensional K { x // x ∈ E2 }\n⊢ FiniteDimensional K { x // x ∈ AlgHom.range (Algebra.TensorProduct.productMap (val E1) (... | [
1111,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.two_le_iff' | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nx : α\n⊢ 2 ≤ (#α) ↔ ∃ y, y ≠ x",
"tactic": "rw [two_le_iff, ← nontrivial_iff, nontrivial_iff_exists_ne x]"
}
] | [
2234,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2233,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.map_cons | [] | [
386,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.mul_lt_of_lt_of_le_one_of_nonneg | [] | [
737,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.surjOn | [] | [
260,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
11
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_le | [] | [
600,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_union' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.333397\nι : Type ?u.333400\nG : Type ?u.333403\nM : Type u_2\nN : Type ?u.333409\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t : Set α\nhst : Disjoint s t\nhs : Set.Finite (s ∩ mulSupport f)\nht : Set.Finite (t... | [
799,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.weaken | [] | [
171,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
11
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_congr | [
{
"state_after": "α✝ : Type ?u.4685\nβ✝ : Type ?u.4688\nγ : Type ?u.4691\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nf : α ≃ β\n⊢ card β = card β",
"state_before": "α✝ : Type ?u.4685\nβ✝ : Type ?u.4688\nγ : Type ?u.4691\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : Fintype... | [
153,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_true | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.54283\nι : Type ?u.54286\ninst✝ : ConditionallyCompleteLattice α\nf : Filter β\nu : β → α\n⊢ (blimsup u f fun x => True) = limsup u f",
"tactic": "simp [blimsup_eq, limsup_eq]"
}
] | [
401,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean | AlgebraicTopology.DoldKan.decomposition_Q | [
{
"state_after": "case zero\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX X' : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.Hom.f (Q Nat.zero) (n + 1) =\n ∑ i in Finset.filter (fun i => ↑i < Nat.zero) Finset.univ,\n HomologicalComplex.Hom.f (P ↑i) (n + 1) ≫\n SimplicialObject.δ ... | [
82,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_cons_of_not_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.36383\nγ : Type ?u.36386\ns t : Multiset α\na : α\nm : ¬a ∈ s\n⊢ s ≤ a ::ₘ t → s ≤ t",
"state_before": "α : Type u_1\nβ : Type ?u.36383\nγ : Type ?u.36386\ns t : Multiset α\na : α\nm : ¬a ∈ s\n⊢ s ≤ a ::ₘ t ↔ s ≤ t",
"tactic": "refine' ⟨_, fun h => le_trans h ... | [
590,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Order/PartialSups.lean | partialSups_zero | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_set | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.61763\nα : Type ?u.61766\nM : Type u_1\nN : Type ?u.61772\nP : Type ?u.61775\nM₀ : Type ?u.61778\nG : Type ?u.61781\nR : Type ?u.61784\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl l₁ l₂ : List M\na✝ x : M\nxs : List M\na : M\n⊢ prod (se... | [
218,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_lt_one_div_of_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.83513\nα : Type u_1\nβ : Type ?u.83519\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nh : a < b\n⊢ 1 / b < 1 / a",
"tactic": "rwa [lt_div_iff' ha, ← div_eq_mul_one_div, div_lt_one (ha.trans h)]"
}
] | [
458,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.colimit_exists_rep | [] | [
210,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.subsingleton.symm | [] | [
214,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
11
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_iSup | [] | [
1259,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/AlgebraicTopology/DoldKan/HomotopyEquivalence.lean | AlgebraicTopology.DoldKan.homotopyPToId_eventually_constant | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq n : ℕ\nhqn : n < q\n⊢ Homotopy.hom (homotopyPToId X (q + 0)) n (n + 1) = Homotopy.hom (homotopyPToId X q) n (n + 1)",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : Simplicia... | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.conj_comp | [] | [
91,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.eq_factors_of_eq_counts | [
{
"state_after": "case intro\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b : Associates α\nha : a ≠ 0\nhb : b ≠ 0\nh : ∀ (p : Associates α), Irreducibl... | [
1502,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
] |
Mathlib/Data/List/MinMax.lean | List.minimum_le_of_mem | [] | [
359,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Algebra/Homology/Augment.lean | CochainComplex.augmentTruncate_inv_f_succ | [] | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.exists_antitone_subbasis | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.96678\nγ : Type ?u.96681\nι : Type ?u.96684\nι' : Sort u_2\nf : Filter α\nh : IsCountablyGenerated f\np : ι' → Prop\ns : ι' → Set α\nhs : HasBasis f p s\nx' : ℕ → Set α\nhx' : f = ⨅ (i : ℕ), 𝓟 (x' i)\n⊢ ∃ x, (∀ (i : ℕ), p (x i)) ∧ HasAntitoneBasis f fun i... | [
1093,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Degeneracies.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.comp_σ | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.24\ninst✝¹ : Category C\ninst✝ : Preadditive C\nY : C\nX : SimplicialObject C\nn b q : ℕ\nφ : Y ⟶ X.obj [n + 1].op\nv : HigherFacesVanish q φ\nhnbq : n + 1 = b + q\n⊢ b < n + 1 + 1",
"tactic": "simp only [hnbq, Nat.lt_add_one_iff, le_add_iff_nonn... | [
55,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.iUnion_subset | [] | [
92,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.IsDiag.isSymm | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.21624\nR : Type ?u.21627\nn : Type u_2\nm : Type ?u.21633\ninst✝ : Zero α\nA : Matrix n n α\nh : IsDiag A\ni j : n\n⊢ Aᵀ i j = A i j",
"state_before": "α : Type u_1\nβ : Type ?u.21624\nR : Type ?u.21627\nn : Type u_2\nm : Type ?u.21633\ninst✝ : Zero α\nA... | [
158,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | antitone_mul_right | [] | [
422,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_id | [] | [
369,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.coe_coe | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.mapsTo_emetric_closedBall | [] | [
172,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_lemma | [
{
"state_after": "F : Type ?u.137488\nι : Type ?u.137491\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.137500\nf✝ : α → β → β\nop : α → α → α\ninst✝¹ : Monoid β\ninst✝ : Monoid γ\ns : Finset α\nf : α → β\ncomm : Set.Pairwise ↑s fun a b => Commute (f a) (f b)\n⊢ Set.Pairwise {x | ∃ a, a ∈ s.val ∧ f a = x} Commute",
... | [
238,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_iff_le_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a / c ≤ b ↔ a ≤ b * c",
"tactic": "rw [← mul_le_mul_iff_right c, div_eq_mul_inv, inv_mul_cancel_right]"
}
] | [
758,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.diagonal_kronecker_diagonal | [] | [
327,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg | [
{
"state_after": "case h\nF : Type ?u.1619749\nα : Type u\nβ : Type v\nγ : Type w\ninst✝ : TopologicalSpace α\nf : α →ᵇ ℝ\nx : α\n⊢ ↑f x = (toReal ∘ ↑(nnrealPart f) - toReal ∘ ↑(nnrealPart (-f))) x",
"state_before": "F : Type ?u.1619749\nα : Type u\nβ : Type v\nγ : Type w\ninst✝ : TopologicalSpace α\nf : α ... | [
1615,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1611,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.paste_vert_iff | [] | [
756,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.TendstoInMeasure.exists_seq_tendstoInMeasure_atTop | [
{
"state_after": "case intro\nα : Type u_2\nι : Type u_1\nE : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : MetricSpace E\nf✝ : ℕ → α → E\ng✝ : α → E\nu : Filter ι\ninst✝¹ : NeBot u\ninst✝ : IsCountablyGenerated u\nf : ι → α → E\ng : α → E\nhfg : TendstoInMeasure μ f u g\nns : ℕ → ι\nh_tendsto_ns : T... | [
252,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.isZero_of_subsingleton | [
{
"state_after": "case h\nR : Type u\ninst✝¹ : Ring R\nM : ModuleCat R\ninst✝ : Subsingleton ↑M\nX : ModuleCat R\nf : M ⟶ X\nx : ↑M\n⊢ ↑f x = ↑default x",
"state_before": "R : Type u\ninst✝¹ : Ring R\nM : ModuleCat R\ninst✝ : Subsingleton ↑M\nX : ModuleCat R\nf : M ⟶ X\n⊢ f = default",
"tactic": "ext x"... | [
224,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/NormedSpace/Completion.lean | UniformSpace.Completion.coe_toComplL | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.injective_subtype | [] | [
440,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | Differentiable.iterate | [] | [
207,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
11
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.ext | [
{
"state_after": "case mk.mk.mk\nι : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁵ : AddCommMonoid ι\ninst✝⁴ : DecidableEq ι\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx : Submonoid A\nc2 : NumDenSameDeg 𝒜 x\ni1 : ι\nn1 : A\nhn1 : n1 ∈ 𝒜 i... | [
116,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_one' | [] | [
633,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | SemiconjBy.cast_nat_mul_right | [] | [
1035,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_eq_zero_iff | [] | [
340,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_abs_toReal_of_sign_nonneg | [
{
"state_after": "no goals",
"state_before": "θ : Angle\nh : 0 ≤ sign θ\n⊢ ↑(abs (toReal θ)) = θ",
"tactic": "rw [abs_eq_self.2 (toReal_nonneg_iff_sign_nonneg.2 h), coe_toReal]"
}
] | [
933,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.symm_symm | [] | [
313,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_mul_right_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : 0 < c\n⊢ ↑(Units.mulRight (Units.mk0 c (_ : c ≠ 0))).symm ⁻¹' Ioo a b = Ioo (a * c) (b * c)",
"tactic": "simp [h, division_def]"
}
] | [
754,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | left_vsub_midpoint | [] | [
119,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.cons_injective_left | [] | [
105,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.trans_source | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.11255\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.11266\nZ : Type u_3\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne✝ : Pretrivialization F proj\nx : Z\ne f : Pretrivialization F proj\n⊢ (LocalEquiv.trans (LocalEquiv.symm ... | [
208,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Control/Traversable/Instances.lean | List.traverse_cons | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toLinearEquiv_symm | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.exists_ball_subset_ball | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.192900\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\nh : y ∈ ball x ε\nthis : 0 < ε - edist y x\n⊢ ∃ ε', ε' > 0 ∧ ball y ε' ⊆ ball x ε",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.192900\ninst✝ : PseudoEMetricSpace α\nx... | [
600,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.isIso_of_components | [] | [
353,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernelZeroIsoSource_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasKernel f\n⊢ 𝟙 X ≫ 0 = 0",
"tactic": "simp"
},
{
"state_after": "case h\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\nin... | [
341,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsGroupHom.trivial_ker_iff_eq_one | [
{
"state_after": "G : Type u_1\nH : Type u_2\nA : Type ?u.115479\na a₁ a₂ b c : G\ninst✝¹ : Group G\ninst✝ : Group H\nf : G → H\nhf : IsGroupHom f\n⊢ (∀ (x : G), x ∈ ker f ↔ x ∈ IsSubgroup.trivial G) ↔ ∀ (x : G), f x = 1 → x = 1",
"state_before": "G : Type u_1\nH : Type u_2\nA : Type ?u.115479\na a₁ a₂ b c ... | [
482,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_unit_zero | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.mul_assoc' | [
{
"state_after": "case coeff.h\nΓ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalSemiring R\nx y z : HahnSeries Γ R\nb : Γ\n⊢ coeff (x * y * z) b = coeff (x * (y * z)) b",
"state_before": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnital... | [
809,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
9
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_sub | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0∞\ny z : ℝ\nhx : x ≠ 0\nh'x : x ≠ ⊤\n⊢ x ^ (y - z) = x ^ y / x ^ z",
"tactic": "rw [sub_eq_add_neg, rpow_add _ _ hx h'x, rpow_neg, div_eq_mul_inv]"
}
] | [
449,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Collinear.coplanar | [] | [
642,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_eq_iSup_norm | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.1017678\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : SeminormedAddCommGroup β\nf g : α →ᵇ β\nx : α\nC : ℝ\n⊢ ‖f‖ = ⨆ (x : α), ‖↑f x‖",
"tactic": "simp_rw [norm_def, dist_eq_iSup, coe_zero, Pi.zero_apply, dist_zero_rig... | [
926,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.coeff_mul | [
{
"state_after": "u : Lean.Level\nR : Type ?u.272248\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nc₂ k a₁ a₂ : ℕ\n⊢ a₁ ^ a₂ * (c₂ * k) = a₁ ^ a₂ * c₂ * k",
"state_before": "u : Lean.Level\nR : Type ?u.272248\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₃ c₂ k a₁ ... | [
744,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.intervalIntegral_tendsto_integral | [
{
"state_after": "ι : Type u_2\nE : Type u_1\nμ : Measure ℝ\nl : Filter ι\ninst✝³ : IsCountablyGenerated l\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\na b : ι → ℝ\nf : ℝ → E\nhfi : Integrable f\nha : Tendsto a l atBot\nhb : Tendsto b l atTop\nφ : ι → Set ℝ := fun i => Ioc ... | [
631,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_pos_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.314784\ninst✝¹ : PseudoEMetricSpace α\nγ : Type w\ninst✝ : EMetricSpace γ\ns : Set γ\n⊢ 0 < diam s ↔ ∃ x, x ∈ s ∧ ∃ y, y ∈ s ∧ x ≠ y",
"tactic": "simp only [diam_pos_iff, Set.Nontrivial, exists_prop]"
}
] | [
1137,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_eq | [] | [
939,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_union_eq_left_of_forall₀ | [] | [
326,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.HasLines.pointCount_le_lineCount | [
{
"state_after": "case pos\nP : Type u_1\nL : Type u_2\ninst✝² : Membership P L\ninst✝¹ : HasLines P L\np : P\nl : L\nh : ¬p ∈ l\ninst✝ : Finite { l // p ∈ l }\nhf : Infinite { p // p ∈ l }\n⊢ pointCount P l ≤ lineCount L p\n\ncase neg\nP : Type u_1\nL : Type u_2\ninst✝² : Membership P L\ninst✝¹ : HasLines P L\... | [
219,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorphOn.mk | [
{
"state_after": "X : Type u_1\nY : Type u_2\nZ : Type ?u.404\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ng : Y → Z\nf : X → Y\ns : Set X\nt : Set Y\nh : ∀ (x : X), x ∈ s → ∃ e, x ∈ e.source ∧ ∀ (y : X), y ∈ e.source → f y = ↑e y\nx : X\nhx : x ∈ s\n⊢ ∃ e, x ∈ e.source... | [
56,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.