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/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_snd_prod | [] | [
936,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.funMap_sumInr | [] | [
307,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Std/Data/Option/Lemmas.lean | Option.bind_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx : Option α\n⊢ Option.bind x some = x",
"tactic": "cases x <;> rfl"
}
] | [
91,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
91,
9
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.InfiniteNeg.not_infinitePos | [] | [
451,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_toNat | [] | [
1587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
] |
Mathlib/Data/PFun.lean | PFun.mem_core_res | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.46763\nδ : Type ?u.46766\nε : Type ?u.46769\nι : Type ?u.46772\nf✝ : α →. β\nf : α → β\ns : Set α\nt : Set β\nx : α\n⊢ x ∈ core (res f s) t ↔ x ∈ s → f x ∈ t",
"tactic": "simp [mem_core, mem_res]"
}
] | [
488,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.lt_succ_sqrt | [] | [
76,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Iso.toEmbedding_completeGraph | [] | [
2011,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2009,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.contDiff | [] | [
234,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
11
] |
Mathlib/Topology/Order/Basic.lean | induced_topology_le_preorder | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\nhf : ∀ {x y : α}, f x < f y ↔ x < y\nx✝ : TopologicalSpace α := Preorder.topology α\n⊢ induced f inst✝¹ ≤ Preorder.topology α",
"state_before": "α ... | [
1017,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | finrank_vectorSpan_insert_le_set | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\np : P\n⊢ finrank k { x // x ∈ vectorSpan k (insert p ↑(affineSpan k s)) } ≤ finrank k { x // x ∈ vectorSpan k s } + 1",
"state_before": "k : ... | [
722,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | smul_vsub_mem_vectorSpan_pair | [] | [
1269,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
] |
Mathlib/Algebra/Order/Positive/Field.lean | Positive.coe_zpow | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.map_comp | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nC : ConnectedComponent G\nφ : G →g G'\nψ : G' →g G''\n⊢ ∀ (v : V), map ψ (map φ (connectedComponentMk G v)) = map (Hom.comp ψ φ) (connectedComponentMk G v)",
"state_before": "V : Type u\nV... | [
2070,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2067,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_le_of_embedding | [] | [
109,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.eq_false_of_ne_true | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ {a : Bool}, a ≠ true → a = false",
"tactic": "decide"
}
] | [
148,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.term_add_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommMonoid α\nn : ℕ\nx a k a' : α\nh : a + k = a'\n⊢ term n x a + k = term n x a'",
"tactic": "simp [h.symm, term, add_assoc]"
}
] | [
136,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powerset_coe' | [] | [
96,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.ofNat_im | [] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.strongTopology.embedding_coeFn | [] | [
110,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Std/Logic.lean | Or.resolve_left | [] | [
268,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
268,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_left_injective | [
{
"state_after": "x : ℝ\nhx : x ≠ 0\ny z : ℝ≥0∞\nhyz : (fun y => y ^ x) y = (fun y => y ^ x) z\n⊢ y = z",
"state_before": "x : ℝ\nhx : x ≠ 0\n⊢ Function.Injective fun y => y ^ x",
"tactic": "intro y z hyz"
},
{
"state_after": "x : ℝ\nhx : x ≠ 0\ny z : ℝ≥0∞\nhyz : y ^ x = z ^ x\n⊢ y = z",
"st... | [
761,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.of_isIso_comp_right | [
{
"state_after": "C : Type u\ninst✝² : Category C\nX✝ Y✝ Z✝ : C\nf✝ g✝ : X✝ ⟶ Y✝\nh : Y✝ ⟶ Z✝\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝¹ : IsIso g\ninst✝ : IsIso (f ≫ g)\n⊢ IsIso ((f ≫ g) ≫ inv g)",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ Z✝ : C\nf✝ g✝ : X✝ ⟶ Y✝\nh : Y✝ ⟶ Z✝\nX Y Z : C\nf : X ... | [
451,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_dvd_gcd_of_dvd_right | [] | [
129,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
128,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | Wbtw.angle₂₁₃_eq_zero_of_ne | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : Wbtw ℝ p₁ p₂ p₃\nhp₂p₁ : p₂ ≠ p₁\n⊢ p₂ -ᵥ p₁ ≠ 0 ∧ ∃ r, 0 < r ∧ p₃ -ᵥ p₁ = r • (p₂ -ᵥ p₁)",
"state_before": "V : Type u_1\nP : T... | [
338,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/CategoryTheory/Abelian/InjectiveResolution.lean | CategoryTheory.InjectiveResolution.ofCocomplex_sq_01_comm | [
{
"state_after": "C : Type u\ninst✝² : Category C\ninst✝¹ : Abelian C\ninst✝ : EnoughInjectives C\nZ : C\n⊢ Injective.ι Z ≫\n (CochainComplex.mkAux (under Z) (syzygies (Injective.ι Z)) (syzygies (d (Injective.ι Z))) (d (Injective.ι Z))\n (d (d (Injective.ι Z)))\n (_ :\n { fst :... | [
282,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_map_left_anticomm | [
{
"state_after": "no goals",
"state_before": "α : Type u_5\nβ : Type u_4\nγ : Type u_3\nf✝ : α → β → γ\na : Option α\nb : Option β\nc : Option γ\nα' : Type u_1\nδ : Type u_2\nf : α' → β → γ\ng : α → α'\nf' : β → α → δ\ng' : δ → γ\nh_left_anticomm : ∀ (a : α) (b : β), f (g a) b = g' (f' b a)\n⊢ map₂ f (Optio... | [
203,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.extendDomain_inv | [] | [
315,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Algebra/Field/Basic.lean | Commute.div_sub_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.44091\nβ : Type ?u.44094\nK : Type u_1\ninst✝ : DivisionRing K\na b c d : K\nhbc : _root_.Commute b c\nhbd : _root_.Commute b d\nhb : b ≠ 0\nhd : d ≠ 0\n⊢ a / b - c / d = (a * d - b * c) / (b * d)",
"tactic": "simpa only [mul_neg, neg_div, ← sub_... | [
194,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
11
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.hasBasis_uniformity_of_basis | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.61464\nι : Type u_3\ns✝ s' : Set α\nx : α\np✝ : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n𝔖 : Set (Set α)\nh : Set.Nonempty 𝔖\nh' : DirectedOn (fun x x_1 => x ⊆ x_1) 𝔖\np : ι → Prop\ns : ι → Set (β × β)\nhb : HasBasis (𝓤 β) p s\n⊢ HasBasis (⨅ (i :... | [
667,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
11
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_nat_cast | [] | [
435,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_add_le | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.1146278\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : AddCommGroup V'\ninst✝ : Module K ... | [
1380,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1373,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.ofSet_eq_refl | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ns✝ : Set α\ninst✝¹ : DecidablePred fun x => x ∈ s✝\ns : Set α\ninst✝ : DecidablePred fun x => x ∈ s\nh : ofSet s = PEquiv.refl α\n⊢ ∀ (x : α), x ∈ s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ns✝ : Set α\ninst✝¹ : Decid... | [
264,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.comap_const | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\nS : Type u\ninst✝¹ : CommRing S\nP : Type u\ninst✝ : CommRing P\nf : R →+* S\nU : Opens ↑(PrimeSpectrum.Top R)\nV : Opens ↑(PrimeSpectrum.Top S)\nhUV : V.carrier ⊆ ↑(PrimeSpectrum.comap f) ⁻¹' U.carrier\na b : R\nhb : ∀ (x : PrimeSpectrum R), x ∈ U → b ∈ Ideal.... | [
1154,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_ge_eq_iInf_nat_add | [] | [
1634,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1633,
1
] |
Mathlib/Topology/Order.lean | induced_top | [] | [
433,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.IsLimit.existsUnique | [] | [
481,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.find?_some_memP | [] | [
164,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
163,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_div_cancel' | [] | [
176,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | Submodule.smul_mem_span_smul | [
{
"state_after": "R : Type u\nS : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : Module R S\ninst✝³ : Module S A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R S A\ninst✝ : SMulCommClass R S A\ns : Set S\nhs : span R s = ⊤\nt : Set A\nk... | [
296,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_mul_succ_div | [
{
"state_after": "α : Type ?u.229103\nβ : Type ?u.229106\nγ : Type ?u.229109\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nh : b ≠ 0\n⊢ a < b * succ (sInf {o | a < b * succ o})",
"state_before": "α : Type ?u.229103\nβ : Type ?u.229106\nγ : Type ?u.229109\nr : α → α → Prop\ns : β → β ... | [
889,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Finset.Nonempty.sup'_eq_cSup_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.39\ninst✝ : ConditionallyCompleteLattice α\ns✝ t : Set α\na✝ b : α\ns : Finset β\nhs : Finset.Nonempty s\nf : β → α\na : α\n⊢ sup' s hs f ≤ a ↔ sSup (f '' ↑s) ≤ a",
"tactic": "simp [csSup_le_iff (s.finite_toSet.image f... | [
31,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.zpow_pos | [] | [
907,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_conjTranspose_iff | [] | [
107,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.adjMatrix_mul_self_apply_self | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.58967\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype V\ninst✝ : NonAssocSemiring α\ni : V\n⊢ (adjMatrix α G ⬝ adjMatrix α G) i i = ↑(degree G i)",
"tactic": "simp [degree]"
}
] | [
249,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Computability/Reduce.lean | OneOneReducible.of_equiv | [] | [
113,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Right.one_lt_mul_of_le_of_lt_of_nonneg | [] | [
899,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.exists_of_lt | [] | [
647,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.rel_join | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.9430\nδ : Type ?u.9433\nr : α → β → Prop\ns : Multiset (Multiset α)\nt : Multiset (Multiset β)\n⊢ Rel r (join 0) (join 0)\n\ncase cons\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.9430\nδ : Type ?u.9433\nr : α → β → Prop\ns : Multiset (Multiset α)... | [
83,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasurableSet.measure_eq_iSup_isCompact_of_ne_top | [] | [
531,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_le_limsup | [] | [
518,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_id_eq | [
{
"state_after": "no goals",
"state_before": "X Y Z : TopCat\n⊢ map (𝟙 X) = 𝟭 (Opens ↑X)",
"tactic": "rfl"
}
] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_val_zero' | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_two_mul' | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cos (2 * x)) = ↑(cos x ^ 2 - sin x ^ 2)",
"tactic": "simp [cos_two_mul']"
}
] | [
1287,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
8
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_eq_zero_iff | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\n⊢ (∀ (x : ℕ), x ∈ support p → coeff p x = 0) ↔ p = 0",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\n⊢ content p = 0 ↔ p = 0"... | [
172,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.toNonneg_coe | [] | [
370,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotoneOn_iff_forall_lt | [] | [
446,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.ofLinearEquiv_toLinearEquiv | [
{
"state_after": "case h\nR : Type u\nA₁ : Type v\nA₂ : Type w\nA₃ : Type u₁\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A₁\ninst✝⁴ : Semiring A₂\ninst✝³ : Semiring A₃\ninst✝² : Algebra R A₁\ninst✝¹ : Algebra R A₂\ninst✝ : Algebra R A₃\ne : A₁ ≃ₐ[R] A₂\nl : A₁ ≃ₗ[R] A₂\nmap_mul✝ : ∀ (x y : A₁), ↑l (x * y) = ↑l ... | [
626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_strictAntiOn | [] | [
613,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.mul_coeff | [] | [
368,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Algebra/Order/Positive/Ring.lean | Positive.val_mul | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.roth_number_eq | [] | [
362,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.next_stop | [
{
"state_after": "no goals",
"state_before": "x✝ : Substring\nh✝ : Valid x✝\nl m r : List Char\nh : ValidFor l m r x✝\n⊢ Substring.next x✝ { byteIdx := Substring.bsize x✝ } = { byteIdx := Substring.bsize x✝ }",
"tactic": "simp [h.bsize, h.next_stop]"
}
] | [
993,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
992,
1
] |
Mathlib/Data/List/Sigma.lean | List.lookupAll_length_le_one | [
{
"state_after": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl : List (Sigma β)\nh : NodupKeys l\nthis : Nodup (map Sigma.fst (map (Sigma.mk a) (lookupAll a l)))\n⊢ length (lookupAll a l) ≤ 1",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\n... | [
317,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Topology/Homotopy/HSpaces.lean | Path.delayReflLeft_one | [
{
"state_after": "no goals",
"state_before": "X : Type u\ninst✝ : TopologicalSpace X\nx y : X\nγ : Path x y\n⊢ delayReflLeft 1 γ = γ",
"tactic": "simp only [delayReflLeft, delayReflRight_one, Path.symm_symm]"
}
] | [
286,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Fintype/Prod.lean | Set.toFinset_off_diag | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.994\nγ : Type ?u.997\ns✝ t s : Set α\ninst✝² : DecidableEq α\ninst✝¹ : Fintype ↑s\ninst✝ : Fintype ↑(offDiag s)\n⊢ ∀ (a : α × α), a ∈ toFinset (offDiag s) ↔ a ∈ Finset.offDiag (toFinset s)",
"tactic": "simp"
}
] | [
42,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Poly.append_denote | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np₁ p₂ : Poly\n⊢ denote ctx (p₁ ++ p₂) = denote ctx p₁ + denote ctx p₂",
"tactic": "match p₁ with\n| [] => simp!\n| v :: p₁ => simp! [append_denote _ p₁ p₂, Nat.add_assoc]"
},
{
"state_after": "no goals",
"state_before": "ctx : Cont... | [
125,
60
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
122,
1
] |
Mathlib/Algebra/Associated.lean | Associated.pow_pow | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.188347\nγ : Type ?u.188350\nδ : Type ?u.188353\ninst✝ : CommMonoid α\na b : α\nh : a ~ᵤ b\n⊢ a ^ Nat.zero ~ᵤ b ^ Nat.zero\n\ncase succ\nα : Type u_1\nβ : Type ?u.188347\nγ : Type ?u.188350\nδ : Type ?u.188353\ninst✝ : CommMonoid α\na b : α\nh : a ~ᵤ b\nn : ... | [
535,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.exists_forall_eventually_atTop_eventually_eq' | [] | [
183,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.exists_lt_map_eq_of_forall_mem | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : LinearOrder α\ninst✝ : Infinite α\nt : Set β\nf : α → β\nhf : MapsTo (fun a => f a) univ t\nht : Set.Finite t\n⊢ ∃ a b, a < b ∧ f a = f b",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : LinearOrder α\ninst... | [
1440,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1436,
1
] |
Mathlib/Data/List/Sublists.lean | List.map_ret_sublist_sublists | [
{
"state_after": "case H0\nα : Type u\nβ : Type v\nγ : Type w\n⊢ [] <+ sublists []\n\ncase H1\nα : Type u\nβ : Type v\nγ : Type w\nl : List α\na : α\nih : map List.ret l <+ sublists l\n⊢ map List.ret l ++ [List.ret a] <+ sublists l ++ map (fun x => x ++ [a]) (sublists l)",
"state_before": "α : Type u\nβ : T... | [
220,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Part.lean | Part.some_append_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.81115\nγ : Type ?u.81118\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"tactic": "simp [append_def]"
}
] | [
820,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_dvd_gcd_mul_left | [] | [
346,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.coe_toMonoidHom | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.IsPushout.IsVanKampen.flip | [
{
"state_after": "J : Type v'\ninst✝¹ : Category J\nC : Type u\ninst✝ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\nH : IsPushout f g h i\nH' : IsVanKampen H\nW' X' Y' Z' : C\nf' : W' ⟶ X'\ng' : W' ⟶ Y'\nh' : X' ⟶ Z'\ni' : Y' ⟶ Z'\nαW : W' ⟶ W\nαX : X' ⟶ Y\nαY : Y' ⟶ X\nαZ : Z' ⟶ Z\nhf ... | [
71,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Std/Logic.lean | not_of_not_imp | [] | [
28,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
28,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.algebraMap_snd | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_factorial | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\nb : ℕ\nx✝ : log p 0 < b\n⊢ multiplicity p 0! = ↑(∑ i in Ico 1 b, 0 / p ^ i)",
"tactic": "simp [Ico, hp.multiplicity_one]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\nn b : ℕ\nhb : log p (n + 1) < b\n... | [
121,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_denom_mul | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\nx y : RatFunc K\n⊢ x * y = ↑(algebraMap K[X] (RatFunc K)) (num x * num y) / ↑(algebraMap K[X] (RatFunc K)) (denom x * denom y)",
"tactic": "conv_lhs =>\n rw [← num_div_denom x, ← num_div_denom y, div_mul_div_comm, ← RingHom.map_... | [
1287,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.refl_toLinearMap | [] | [
479,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_inf | [] | [
860,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.nthRoots_nodup | [
{
"state_after": "case inl\nM : Type ?u.3600187\nN : Type ?u.3600190\nG : Type ?u.3600193\nR : Type u_1\nS : Type ?u.3600199\nF : Type ?u.3600202\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh✝ : IsPrimitiveRoot ζ✝ k\ninst✝ : IsDomain R\nζ ... | [
859,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Order/PropInstances.lean | Prop.disjoint_iff | [] | [
102,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/Separation.lean | separated_by_continuous | [] | [
1123,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | Metric.exists_continuous_real_forall_closedBall_subset | [] | [
149,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | lt_of_mul_self_lt_mul_self | [
{
"state_after": "β : Type ?u.245753\nA : Type ?u.245756\nG : Type ?u.245759\nM : Type ?u.245762\nR : Type u_1\ninst✝ : LinearOrderedSemiring R\na b : R\nhb : 0 ≤ b\n⊢ a ^ 2 < b ^ 2 → a < b",
"state_before": "β : Type ?u.245753\nA : Type ?u.245756\nG : Type ?u.245759\nM : Type ?u.245762\nR : Type u_1\ninst✝... | [
621,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence | [
{
"state_after": "C : Type u_3\nD : Type u_4\ninst✝² : Category C\ninst✝¹ : Category D\nF : C ⥤ D\ninst✝ : IsEquivalence F\nh : HasStrongEpiMonoFactorisations C\nX Y : D\nf : X ⟶ Y\nem : StrongEpiMonoFactorisation ((inv F).map f) :=\n Nonempty.some (_ : Nonempty (StrongEpiMonoFactorisation ((inv F).map f)))\n⊢... | [
1063,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.two_lt_card_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.24655\nγ : Type ?u.24658\ninst✝¹ : Fintype α\ninst✝ : Fintype β\n⊢ 2 < card α ↔ ∃ a b c, a ≠ b ∧ a ≠ c ∧ b ≠ c",
"tactic": "simp_rw [← Finset.card_univ, two_lt_card_iff, mem_univ, true_and_iff]"
}
] | [
601,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
8
] |
Mathlib/Data/Complex/Module.lean | Complex.liftAux_I | [] | [
387,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.emem_iff_all | [] | [
490,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/LinearAlgebra/DirectSum/Finsupp.lean | finsuppTensorFinsupp_symm_single | [] | [
87,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.of_sections | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.141298\nδ : Type ?u.141301\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf✝ f : α → β\nh : ∀ (x : α), ∃ g, ContinuousAt g (f x) ∧ g (f x) = x ∧ Function.RightInverse g f\nx : α\ng :... | [
393,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.iff_ne_zero | [
{
"state_after": "R : Type u_1\ninst✝ : MonoidWithZero R\nf : ArithmeticFunction R\nm n : ℕ\nh : m ≠ 0 → n ≠ 0 → coprime m n → ↑f (m * n) = ↑f m * ↑f n\nhmn : coprime m n\n⊢ ↑f (m * n) = ↑f m * ↑f n",
"state_before": "R : Type u_1\ninst✝ : MonoidWithZero R\nf : ArithmeticFunction R\n⊢ IsMultiplicative f ↔ ↑... | [
719,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.const_pow | [] | [
249,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.refl' | [] | [
82,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.add | [] | [
537,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comapEquiv_symm_coe | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/List/Basic.lean | List.getI_cons_succ | [] | [
4468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4467,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.HasBasis.uniformEquicontinuous_iff_right | [
{
"state_after": "ι : Type u_3\nκ✝ : Type ?u.126986\nX : Type ?u.126989\nY : Type ?u.126992\nZ : Type ?u.126995\nα : Type u_2\nβ : Type u_4\nγ : Type ?u.127004\n𝓕 : Type ?u.127007\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSp... | [
322,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_eq_default | [
{
"state_after": "case nil\nι : Type ?u.502171\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nx : α\nxs : List α\nd : α\nn✝¹ n✝ : ℕ\nhn✝ : length l ≤ n✝\nn : ℕ\nhn : length [] ≤ n\n⊢ getD [] n d = d\n\ncase cons\nι : Type ?u.502171\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : L... | [
4407,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4402,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.