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/Order/BoundedOrder.lean | StrictMono.apply_eq_top_iff | [] | [
200,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | BoundedContinuousFunction.toLp_norm_le | [] | [
1671,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1669,
1
] |
Mathlib/Algebra/Category/GroupCat/Biproducts.lean | AddCommGroupCat.binaryProductLimitCone_cone_π_app_right | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/BooleanAlgebra.lean | eq_compl_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.54408\nw x y z : α\ninst✝ : BooleanAlgebra α\n⊢ x = yᶜ ↔ y = xᶜ",
"tactic": "rw [eq_comm, compl_eq_iff_isCompl, eq_compl_iff_isCompl]"
}
] | [
632,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.withSeminorms_of_hasBasis | [] | [
431,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | Measurable.lintegral_prod_left' | [] | [
276,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xy_succ_succ | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\nthis : pellZd a1 (n + 2) + pellZd a1 n = ↑(2 * a) * pellZd a1 (n + 1)\n⊢ xn a1 (n + 2) + xn a1 n = 2 * a * xn a1 (n + 1) ∧ yn a1 (n + 2) + yn a1 n = 2 * a * yn a1 (n + 1)",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ xn a1 (n + 2) + xn a1 n = 2 * a * xn a1 (n + 1... | [
528,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.list_sum_mem | [] | [
378,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
11
] |
Mathlib/Data/Multiset/Pi.lean | Multiset.Pi.cons_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nβ : α → Type u\nδ : α → Sort v\na : α\nb : δ a\ns : Multiset α\nhs : ¬a ∈ s\nf₁ f₂ : (a : α) → a ∈ s → δ a\neq : cons s a b f₁ = cons s a b f₂\na' : α\nh' : a' ∈ s\nne : a ≠ a'\nthis : a' ∈ a ::ₘ s\n⊢ f₁ a' h' = cons s a b f₁... | [
83,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_lt | [] | [
252,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.coe_toBotHom | [] | [
738,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_atBot_eq | [] | [
360,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.w_map_wMk | [
{
"state_after": "n : ℕ\nP : MvPFunctor (n + 1)\nα β : TypeVec n\ng : α ⟹ β\na : P.A\nf' : B (drop P) a ⟹ α\nf : PFunctor.B (last P) a → W P α\n⊢ g <$$> wMk P a f' f = wMk P a (g ⊚ f') (MvFunctor.map g ∘ f)",
"state_before": "n : ℕ\nP : MvPFunctor (n + 1)\nα β : TypeVec n\ng : α ⟹ β\na : P.A\nf' : B (drop P... | [
269,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_injective | [] | [
192,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Deprecated/Group.lean | IsGroupHom.mul | [] | [
344,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.map_comp_lTensor | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1285748\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1285754\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_4\nP : Type u_3\nQ : Type u_5\nS : Type u_6\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ :... | [
1137,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.map | [] | [
268,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
11
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_trailingCoeff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\nhu : u ≠ 0\n⊢ trailingCoeff (trinomial k m n u v w) = u",
"tactic": "rw [trailingCoeff, trinomial_natTrailingDegree hkm hmn hu, trinomial_trailing_coeff' hkm hmn]"
}
] | [
105,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.map_bind | [] | [
79,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.fst_smul | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_sub_left_lt | [
{
"state_after": "a b c : Int\nh✝ : a - b < c\nh : a - b + b < c + b\n⊢ a < b + c",
"state_before": "a b c : Int\nh : a - b < c\n⊢ a < b + c",
"tactic": "have h := Int.add_lt_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a - b < c\nh : a - b + b < c + b\n⊢... | [
1073,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1071,
11
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean | measurable_of_tendsto_metrizable_ae | [] | [
147,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.two_le_card_support | [] | [
384,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_eq_zero_of_lt | [
{
"state_after": "α : Type ?u.243145\nβ : Type ?u.243148\nγ : Type ?u.243151\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nh : a < b\n⊢ a < b * succ 0",
"state_before": "α : Type ?u.243145\nβ : Type ?u.243148\nγ : Type ?u.243151\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\n... | [
952,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.segment_subset | [] | [
70,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.ext | [] | [
59,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_congr | [] | [
1531,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.eventually_cofinite | [] | [
2645,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2644,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_zero_eq | [] | [
673,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.le_cof_iff_lsub | [
{
"state_after": "α : Type ?u.28294\nr : α → α → Prop\no : Ordinal\na : Cardinal\n⊢ a ≤ sInf {a | ∃ ι f, lsub f = o ∧ (#ι) = a} ↔ ∀ {ι : Type u} (f : ι → Ordinal), lsub f = o → a ≤ (#ι)",
"state_before": "α : Type ?u.28294\nr : α → α → Prop\no : Ordinal\na : Cardinal\n⊢ a ≤ cof o ↔ ∀ {ι : Type u} (f : ι → O... | [
327,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_injective | [] | [
465,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_id | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁹ : CommRing R\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nN : Type ?u.396174\ninst✝⁶ : AddCommGroup N\ninst✝⁵ : Module R N\nι : Type ?u.396716\ninst✝⁴ : Module.Free R M\ninst✝³ : Module.Finite R M\ninst✝² : Module.Free R N\ni... | [
197,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_nil_right | [
{
"state_after": "α : Type u_1\nl : List α\n⊢ Disjoint [] l",
"state_before": "α : Type u_1\nl : List α\n⊢ Disjoint l []",
"tactic": "rw [disjoint_comm]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ Disjoint [] l",
"tactic": "exact disjoint_nil_left _"
}... | [
1376,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1375,
9
] |
Mathlib/Order/Filter/Basic.lean | Filter.inter_eventuallyEq_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.190687\nι : Sort x\ns t : Set α\nl : Filter α\n⊢ s ∩ t =ᶠ[l] t ↔ ∀ᶠ (x : α) in l, x ∈ t → x ∈ s",
"tactic": "rw [inter_comm, inter_eventuallyEq_left]"
}
] | [
1597,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.image | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u\nβ : Type v\nι : Type ?u.21179\nπ : ι → Type ?u.21184\ninst✝¹ : TopologicalSpace α\ns✝ t u✝ v✝ : Set α\ninst✝ : TopologicalSpace β\ns : Set α\nH : IsPreconnected s\nf : α → β\nhf : ContinuousOn f s\nu v : Set β\nhu : IsOpen u\nhv... | [
334,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
11
] |
Std/Data/Int/Lemmas.lean | Int.pos_of_sign_eq_one | [] | [
1280,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1279,
1
] |
Mathlib/Algebra/Group/Defs.lean | CommGroup.toGroup_injective | [
{
"state_after": "case mk.mk.refl\nG✝ : Type ?u.58954\nG : Type u\ntoGroup✝ : Group G\nmul_comm✝¹ mul_comm✝ : ∀ (a b : G), a * b = b * a\n⊢ mk mul_comm✝¹ = mk mul_comm✝",
"state_before": "G✝ : Type ?u.58954\nG : Type u\n⊢ Injective (@toGroup G)",
"tactic": "rintro ⟨⟩ ⟨⟩ ⟨⟩"
},
{
"state_after": "... | [
1164,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_div | [] | [
229,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.110349\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nx✝² : NonAssocSemiring α\nx✝¹ : NonAssocSemiring β\nx✝ : NonAssocSemiring γ\ng : β →+* γ\nf₁ f₂ : α →+* β\nhg : Injective ↑g\nh : comp g f₁ = comp g f₂\nx : α\n⊢ ↑g (↑f₁ x) = ↑g (↑f₂ x)",
"tactic"... | [
754,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Topology/StoneCech.lean | ultrafilter_extend_eq_iff | [
{
"state_after": "α : Type u\nγ : Type u_1\ninst✝² : TopologicalSpace γ\ninst✝¹ : T2Space γ\ninst✝ : CompactSpace γ\nf : α → γ\nb : Ultrafilter α\nc : γ\nh : Ultrafilter.extend f b = c\nb' : Ultrafilter (Ultrafilter α) := Ultrafilter.map pure b\n⊢ ↑(Ultrafilter.map f b) ≤ 𝓝 c",
"state_before": "α : Type u\... | [
212,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_bihimp_cancel_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.82316\nα : Type u_1\nβ : Type ?u.82322\nπ : ι → Type ?u.82327\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ⇔ (a ⇔ b) = b",
"tactic": "simp [← bihimp_assoc]"
}
] | [
645,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | Int.ModEq.pow_card_sub_one_eq_one | [
{
"state_after": "K : Type ?u.1090717\nR : Type ?u.1090720\np : ℕ\nhp : Nat.Prime p\nn : ℤ\nhpn : IsCoprime n ↑p\nthis : Fact (Nat.Prime p)\n⊢ n ^ (p - 1) ≡ 1 [ZMOD ↑p]",
"state_before": "K : Type ?u.1090717\nR : Type ?u.1090720\np : ℕ\nhp : Nat.Prime p\nn : ℤ\nhpn : IsCoprime n ↑p\n⊢ n ^ (p - 1) ≡ 1 [ZMOD ... | [
464,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_inf | [] | [
1537,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1536,
1
] |
Mathlib/Topology/ContinuousOn.lean | mem_nhds_subtype_iff_nhdsWithin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.304019\nγ : Type ?u.304022\nδ : Type ?u.304025\ninst✝ : TopologicalSpace α\ns : Set α\na : ↑s\nt : Set ↑s\n⊢ t ∈ 𝓝 a ↔ Subtype.val '' t ∈ 𝓝[s] ↑a",
"tactic": "rw [← map_nhds_subtype_val, image_mem_map_iff Subtype.val_injective]"
... | [
503,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.not_sOppSide_self | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.231207\nP : Type u_3\nP' : Type ?u.231213\ninst✝⁶ : LinearOrderedField 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 : AffineSubspace R P\nx : P\n⊢ ¬(W... | [
435,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.eventually_prod_nhds_iff | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.93290\nι : Type u_1\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nf : Filter ι\nx₀ : α\np : ι × α → Prop\n⊢ (∃ ε, ε > 0 ∧ ∃ pa, (∀ᶠ (i : ι) in f, pa i) ∧ ∀ {x : α}, dist x x₀ < ε → ∀ {i : ι}, pa i → p (Prod.swap (x, i))) ↔\n ∃ pa, (∀ᶠ... | [
977,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Order/WithBot.lean | WithBot.toDual_apply_coe | [] | [
944,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_div | [
{
"state_after": "case inl\nm : ℕ\n⊢ ↑(m / 0) = ↑m / ↑0\n\ncase inr\nm n : ℕ\nhn : n ≠ 0\n⊢ ↑(m / n) = ↑m / ↑n",
"state_before": "m n : ℕ\n⊢ ↑(m / n) = ↑m / ↑n",
"tactic": "rcases eq_or_ne n 0 with (rfl | hn)"
},
{
"state_after": "no goals",
"state_before": "case inl\nm : ℕ\n⊢ ↑(m / 0) = ↑m ... | [
2352,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2343,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.HasFiniteBiproducts.of_hasFiniteProducts | [] | [
194,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.gcd_eq_zero_iff | [
{
"state_after": "case mp\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns : Multiset α\n⊢ gcd s = 0 → ∀ (x : α), x ∈ s → x = 0\n\ncase mpr\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns : Multiset α\n⊢ (∀ (x : α), x ∈ s → x = 0) → gcd s ... | [
185,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/Convex/Normed.lean | convex_ball | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.20959\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\na : E\nr : ℝ\n⊢ Convex ℝ (ball a r)",
"tactic": "simpa only [Metric.ball, sep_univ] using (convexOn_univ_dist a).convex_lt r"
}
] | [
66,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.support_bernoulli | [
{
"state_after": "α : Type ?u.168514\nβ : Type ?u.168517\nγ : Type ?u.168520\np : ℝ≥0∞\nh : p ≤ 1\nb✝ b : Bool\n⊢ b ∈ support (bernoulli p h) ↔ b ∈ {b | bif b then p ≠ 0 else p ≠ 1}",
"state_before": "α : Type ?u.168514\nβ : Type ?u.168517\nγ : Type ?u.168520\np : ℝ≥0∞\nh : p ≤ 1\nb : Bool\n⊢ support (berno... | [
321,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_neg | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a - -b = a + b",
"tactic": "simp [Int.sub_eq_add_neg]"
}
] | [
369,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
369,
11
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | affineIndependent_iff_not_finrank_vectorSpan_le | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_4\nι : Type u_1\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : Fintype ι\np : ι → P\nn : ℕ\nhc : Fintype.card ι = n + 2\n⊢ AffineIndependent k p ↔ ¬finrank k { x //... | [
199,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_sq | [
{
"state_after": "x y : ℝ\n⊢ ↑(sinh x ^ 2) = ↑(cosh x ^ 2 - 1)",
"state_before": "x y : ℝ\n⊢ sinh x ^ 2 = cosh x ^ 2 - 1",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(sinh x ^ 2) = ↑(cosh x ^ 2 - 1)",
"tactic": "simp [sinh_sq]"
}
] | [
1441,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1441,
8
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.top_prod_top | [] | [
1079,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.neg_apply | [] | [
466,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Topology/Constructions.lean | isClosedMap_ofDual | [] | [
175,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_le_toNNReal_iff | [
{
"state_after": "no goals",
"state_before": "r p : ℝ\nhp : 0 ≤ p\n⊢ toNNReal r ≤ toNNReal p ↔ r ≤ p",
"tactic": "simp [← NNReal.coe_le_coe, hp]"
}
] | [
631,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.tan_add | [
{
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118,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/ShrinkingLemma.lean | ShrinkingLemma.PartialRefinement.exists_gt | [
{
"state_after": "ι : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nu : ι → Set X\ns : Set X\nv : PartialRefinement u s\nhs : IsClosed s\ni : ι\nhi : ¬i ∈ v.carrier\nI : (s ∩ ⋂ (j : ι) (_ : j ≠ i), toFun v jᶜ) ⊆ toFun v i\n⊢ ∃ v', v < v'",
"state_before": "ι : Type u_1\nX : Typ... | [
207,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.dvd_iff_not_coprime | [] | [
550,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mul_unit_mem_iff_mem | [] | [
495,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.natAbs_inj_of_nonpos_of_nonpos | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\nha : a ≤ 0\nhb : b ≤ 0\n⊢ natAbs a = natAbs b ↔ a = b",
"tactic": "simpa only [Int.natAbs_neg, neg_inj] using\n natAbs_inj_of_nonneg_of_nonneg (neg_nonneg_of_nonpos ha) (neg_nonneg_of_nonpos hb)"
}
] | [
71,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.even_sub' | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nh : n ≤ m\n⊢ Even (m - n) ↔ (Odd m ↔ Odd n)",
"tactic": "rw [even_sub h, even_iff_not_odd, even_iff_not_odd, not_iff_not]"
}
] | [
147,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.mk_lt_mk | [] | [
145,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
145,
9
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.extendDomain_apply_not_subtype | [
{
"state_after": "no goals",
"state_before": "α' : Type u_2\nβ' : Type u_1\ne : Perm α'\np : β' → Prop\ninst✝ : DecidablePred p\nf : α' ≃ Subtype p\nb : β'\nh : ¬p b\n⊢ ↑(extendDomain e f) b = b",
"tactic": "simp [Perm.extendDomain, h]"
}
] | [
1450,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.mem_atomise | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nF : Finset (Finset α)\n⊢ t ∈ (atomise s F).parts ↔ Finset.Nonempty t ∧ ∃ Q x, filter (fun i => ∀ (u : Finset α), u ∈ F → (u ∈ Q ↔ i ∈ u)) s = t",
"tactic": "simp only [atomise, ofErase,... | [
566,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsLocalization.localization_localization_isLocalization | [] | [
129,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_comp | [
{
"state_after": "case H.h.h\nR : Type u_4\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1235162\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1235168\ninst✝¹² : Semiring R''\nM : Type u_1\nN : Type u_2\nP : Type u_5\nQ : Type u_3\nS : Type ?u.1235186\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoi... | [
1068,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.pentagon_inv | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V W✝ X✝ Y✝ Z✝ W X Y Z : C\n⊢ inv ((𝟙 W ⊗ (α_ X Y Z).inv) ≫ (α_ W (X ⊗ Y) Z).inv ≫ ((α_ W X Y).inv ⊗ 𝟙 Z)) =\n inv ((α_ W X (Y ⊗ Z)).i... | [
287,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.cond_not | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nb : Bool\nt e : α\n⊢ (bif !b then t else e) = bif b then e else t",
"tactic": "cases b <;> rfl"
}
] | [
136,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.apply | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
11
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.right_comm | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type ?u.296946\ninst✝⁵ : CommSemiring R\ninst✝⁴ : CommSemiring S\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nx : A\nr : R\ny : A\n⊢ x * ↑(algebraMap R A) r * y = x * y * ↑(algebraM... | [
379,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.sourceHomeomorphBaseSetProd_apply | [] | [
485,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Topology/Connected.lean | preconnectedSpace_iff_connectedComponent | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Type ?u.63690\nπ : ι → Type ?u.63695\ninst✝ : TopologicalSpace α\ns t u v : Set α\n⊢ PreconnectedSpace α → ∀ (x : α), connectedComponent x = univ\n\ncase mpr\nα : Type u\nβ : Type v\nι : Type ?u.63690\nπ : ι → Type ?u.63695\ninst✝ : TopologicalSpace α\ns t ... | [
792,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | parallelepiped_single | [
{
"state_after": "case h\nι : Type u_1\nι' : Type ?u.104527\nE : Type ?u.104530\nF : Type ?u.104533\ninst✝⁶ : Fintype ι\ninst✝⁵ : Fintype ι'\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : AddCommGroup F\ninst✝¹ : Module ℝ F\ninst✝ : DecidableEq ι\na x : ι → ℝ\n⊢ (x ∈ parallelepiped fun i => Pi.single i... | [
182,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.map_on | [] | [
136,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.empty | [] | [
74,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Units.embedding_val | [] | [
1751,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1749,
16
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.elim_singleton | [] | [
89,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.degree_eq_degree_of_associated | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nh : Associated p q\nu : R[X]ˣ\nhu : p * ↑u = q\n⊢ degree p = degree q",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q... | [
989,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
987,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.piecewise_erase_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.23061\nγ : Type ?u.23064\ninst✝¹ : Fintype α\ns t : Finset α\nδ : α → Sort u_1\ninst✝ : DecidableEq α\na : α\nf g : (a : α) → δ a\n⊢ piecewise (erase univ a) f g = update f a (g a)",
"tactic": "rw [← compl_singleton, piecewise_compl... | [
299,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integral_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[... | [
299,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_const | [] | [
499,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.coe_autToPow_apply | [] | [
985,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.mul_eq | [] | [
67,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.sigma_zero_apply_prime_pow | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.525397\np i : ℕ\nhp : Prime p\n⊢ ↑(σ 0) (p ^ i) = i + 1",
"tactic": "rw [sigma_zero_apply, divisors_prime_pow hp, card_map, card_range]"
}
] | [
795,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.union_symm_apply_left | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Ring.mul_inverse_rev | [] | [
41,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | sub_smul_dslope | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf✝ : 𝕜 → E\na✝ b✝ : 𝕜\ns : Set 𝕜\nf : 𝕜 → E\na b : 𝕜\n⊢ (b - a) • dslope f a b = f b - f a",
"tactic": "rcases eq_or_ne b a with (... | [
72,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.inl_lt_inl_iff | [] | [
356,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.principal_F | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/Associated.lean | associated_mul_unit_right | [] | [
466,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.rank_bot | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nK L : IntermediateField F E\n⊢ Module.rank F { x // x ∈ ⊥ } = 1",
"tactic": "rw [rank_eq_one_iff]"
}
] | [
724,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux | [
{
"state_after": "case zero\nn✝¹ : Type ?u.315793\np : Type ?u.315796\nR : Type u₂\n𝕜 : Type u_1\ninst✝⁹ : Field 𝕜\ninst✝⁸ : DecidableEq n✝¹\ninst✝⁷ : DecidableEq p\ninst✝⁶ : CommRing R\nr : ℕ\nM✝¹ : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜\ninst✝⁵ : Fintype n✝¹\ninst✝⁴ : Fintype p\nn✝ : Type\ninst✝³ : Fintype... | [
668,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf✝ f : R →+* S\nhf : ↑f (leadingCoeff p) ≠ 0\n⊢ coeff (map f p) (natDegree (map f p)) = ↑f (coeff p (natDegree p))",
"state_before": "R : Type u\nS : Type v\nT : Type w\... | [
890,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Algebra/Field/Basic.lean | div_neg | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.35372\nβ : Type ?u.35375\nK : Type u_1\ninst✝¹ : DivisionMonoid K\ninst✝ : HasDistribNeg K\na✝ b a : K\n⊢ a / -b = -(a / b)",
"tactic": "rw [← div_neg_eq_neg_div]"
}
] | [
130,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | eventually_mapsTo_of_isCompact_absorbing_of_isOpen_of_omegaLimit_subset | [
{
"state_after": "case intro.intro\nτ : Type u_2\nα : Type u_3\nβ : Type u_1\nι : Type ?u.73083\ninst✝¹ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\ninst✝ : T2Space β\nc : Set β\nhc₁ : IsCompact c\nhc₂ : ∀ᶠ (t : τ) in f, MapsTo (ϕ t) s c\nn : Set β\nhn₁ : IsOpen n\nhn₂ : ω f ϕ s ⊆ n\nu : ... | [
290,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.dom_of_le_natCast | [
{
"state_after": "no goals",
"state_before": "x : PartENat\ny : ℕ\nh : x ≤ ↑y\n⊢ x.Dom",
"tactic": "exact dom_of_le_some h"
}
] | [
221,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
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