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/LinearAlgebra/Eigenspace/Basic.lean | Module.End.mem_eigenspace_iff | [
{
"state_after": "no goals",
"state_before": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End R M\nμ : R\nx : M\n⊢ x ∈ eigenspace f μ ↔ ↑f x = μ • x",
"tactic": "rw [eigenspace, LinearMa... | [
100,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.continuantsAux_eq_continuantsAux_squashGCF_of_le | [
{
"state_after": "K : Type u_1\nn : ℕ\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\n⊢ ∀ (n_1 : ℕ),\n (∀ (m : ℕ), m < n_1 → m ≤ n → continuantsAux g m = continuantsAux (squashGCF g n) m) →\n n_1 ≤ n → continuantsAux g n_1 = continuantsAux (squashGCF g n) n_1",
... | [
261,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.sum_add_distrib | [
{
"state_after": "α β : Type u\nι : Type u_1\nf g : ι → Cardinal\nthis :\n (#(i : ι) × ((Quotient.out ∘ f) i ⊕ (Quotient.out ∘ g) i)) =\n (#(i : ι) × (Quotient.out ∘ f) i ⊕ (i : ι) × (Quotient.out ∘ g) i)\n⊢ sum (f + g) = sum f + sum g",
"state_before": "α β : Type u\nι : Type u_1\nf g : ι → Cardinal\n⊢... | [
888,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_of_monotone_of_subseq | [] | [
1739,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Mathlib/Order/Synonym.lean | OrderDual.toDual_lt | [] | [
125,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.curry_apply | [] | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/Concept.lean | Concept.strictMono_fst | [] | [
259,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.convergents'_succ | [
{
"state_after": "case inl\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nh : fract v = 0\n⊢ convergents' (of v) (n + 1) = ↑⌊v⌋ + 1 / convergents' (of (fract v)⁻¹) n\n\ncase inr\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nh : fract v ≠ 0\n⊢ ... | [
349,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Order/Hom/Order.lean | OrderHom.coe_iSup | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_2\ninst✝¹ : Preorder α\nι : Sort u_1\ninst✝ : CompleteLattice β\nf : ι → α →o β\nx : α\n⊢ ↑(⨆ (i : ι), f i) x = iSup (fun i => ↑(f i)) x",
"state_before": "α : Type u_3\nβ : Type u_2\ninst✝¹ : Preorder α\nι : Sort u_1\ninst✝ : CompleteLattice β\nf : ι → α →... | [
122,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow_of_lt_left | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.224581\nA : Type ?u.224584\nG : Type ?u.224587\nM : Type ?u.224590\nR : Type u_1\ninst✝ : StrictOrderedSemiring R\na x y : R\nn m : ℕ\nh : x < y\nhx : 0 ≤ x\nhn : 0 < 0\n⊢ x ^ 0 < y ^ 0",
"tactic": "contradiction"
},
{
"state_after": "no ... | [
488,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictFDerivAt.ccosh | [] | [
442,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Order/PropInstances.lean | Pi.codisjoint_iff | [] | [
90,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_nonpos_of_nonpos_of_nonneg | [] | [
94,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_append | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\ns1 s2 : WSeq α\nt1 t2 : WSeq β\nh1 : LiftRel R s1 t1\nh2 : LiftRel R s2 t2\ns✝ : WSeq α\nt✝ : WSeq β\nh✝ : (fun s t => LiftRel R s t ∨ ∃ s1 t1, s = append s1 s2 ∧ t = append t1 t2 ∧ LiftRel R s1 t1) s✝ t✝\ns : WSeq α\nt : WSeq β\nh : LiftRe... | [
1586,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1560,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.map_comp | [] | [
347,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean | AbsoluteValue.IsAdmissible.exists_partition | [
{
"state_after": "R : Type u_2\ninst✝¹ : EuclideanDomain R\nabv : AbsoluteValue R ℤ\nι : Type u_1\ninst✝ : Fintype ι\nε : ℝ\nhε : 0 < ε\nb : R\nhb : b ≠ 0\nA : ι → R\nh : IsAdmissible abv\ne : ι ≃ Fin (Fintype.card ι) := Fintype.equivFin ι\n⊢ ∃ t, ∀ (i₀ i₁ : ι), t i₀ = t i₁ → ↑(↑abv (A i₁ % b - A i₀ % b)) < ↑ab... | [
72,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Ioc' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.100377\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\nx : α\n⊢ x ∈ Iic b ∪ Ioc c d ↔ x ∈ Iic (max b d)",
"state_before": "α : Type u_1\nβ : Type ?u.100377\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\n⊢ Iic b ∪ Ioc c d = Iic (m... | [
1414,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
1
] |
Mathlib/Data/ULift.lean | PLift.down_bijective | [] | [
66,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | one_le_sq_iff_one_le_abs | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.269979\nA : Type ?u.269982\nG : Type ?u.269985\nM : Type ?u.269988\nR : Type u_1\ninst✝ : LinearOrderedRing R\nx✝ y x : R\n⊢ 1 ≤ x ^ 2 ↔ 1 ≤ abs x",
"tactic": "simpa only [one_pow, abs_one] using @sq_le_sq _ _ 1 x"
}
] | [
741,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.add_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.173480\np : PosNum\n⊢ pos p + 1 = succ (pos p)",
"tactic": "cases p <;> rfl"
}
] | [
218,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_inj' | [
{
"state_after": "no goals",
"state_before": "V : Type u\ninst✝ : Quiver V\na b c d : V\np₁ p₂ : Path a b\nq₁ q₂ : Path b c\nh : length p₁ = length p₂\nh_eq : comp p₁ q₁ = comp p₂ q₂\n⊢ ?m.9164 h h_eq + length q₁ = ?m.9164 h h_eq + length q₂",
"tactic": "simpa [h] using congr_arg length h_eq"
},
{
... | [
144,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/Separation.lean | t2_iff_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : TopologicalSpace α\n⊢ T2Space α ↔ ∀ {x y : α}, NeBot (𝓝 x ⊓ 𝓝 y) → x = y",
"tactic": "simp only [t2Space_iff_disjoint_nhds, disjoint_iff, neBot_iff, Ne.def, not_imp_comm]"
}
] | [
923,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.comp_id | [
{
"state_after": "no goals",
"state_before": "M' : Type ?u.269528\nX : Type ?u.269531\ninst✝²³ : SMul M' X\nY : Type ?u.269538\ninst✝²² : SMul M' Y\nZ : Type ?u.269545\ninst✝²¹ : SMul M' Z\nM : Type u_1\ninst✝²⁰ : Monoid M\nA : Type ?u.269558\ninst✝¹⁹ : AddMonoid A\ninst✝¹⁸ : DistribMulAction M A\nA' : Type... | [
572,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.toTopologicalSpace_injective | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝ : Group α\ng : GroupTopology α\ntoTopologicalSpace✝ : TopologicalSpace α\ntoTopologicalGroup✝ : TopologicalGroup α\nh :\n { toTopologicalSpace := toTopologicalSpace✝, toTopologicalGroup := toTopologicalGroup✝ }.toTopologicalSpace ... | [
1878,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1873,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHomClass.monotone | [] | [
157,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
11
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.bot_add | [] | [
580,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Init/Logic.lean | ExistsUnique.intro | [] | [
235,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.refl | [] | [
828,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_inter | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf✝ : Y ⟶ X\nS✝ R✝ : Sieve X\nf : Y ⟶ X\nS R : Sieve X\n⊢ pullback f (S ⊓ R) = pullback f S ⊓ pullback f R",
"tactic": "simp [Sieve.ext_iff]"
}
] | [
478,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.symm | [] | [
391,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
11
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuous_of_continuousAt_one₂ | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH✝ : Type x\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalGroup G\ninst✝⁶ : TopologicalSpace α\nf✝ : α → G\ns : Set α\nx✝¹ : α\nH : Type u_1\nM : Type u_2\ninst✝⁵ : CommMonoid M\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ContinuousMul M\nin... | [
887,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_le_succ_sub | [
{
"state_after": "no goals",
"state_before": "a i : Nat\n⊢ a - i ≤ succ a - i",
"tactic": "cases i with\n| zero => apply Nat.le_of_lt; apply Nat.lt_succ_self\n| succ i => rw [Nat.sub_succ, Nat.succ_sub_succ]; apply Nat.pred_le"
},
{
"state_after": "case zero.h\na : Nat\n⊢ a - zero < succ a - zer... | [
545,
70
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
542,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.eq_pthRoot | [
{
"state_after": "case mk\nK : Type u\ninst✝² : Field K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nm : ℕ\nx : K\n⊢ mk K p (m, x) = (↑(pthRoot (PerfectClosure K p) p)^[(m, x).fst]) (↑(of K p) (m, x).snd)",
"state_before": "K : Type u\ninst✝² : Field K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ :... | [
545,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.inv_le | [
{
"state_after": "no goals",
"state_before": "r p : ℝ≥0\nh : r ≠ 0\n⊢ r⁻¹ ≤ p ↔ 1 ≤ r * p",
"tactic": "rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h]"
}
] | [
782,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.gfp_le_map | [] | [
136,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.neg_right | [] | [
1256,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1254,
1
] |
Mathlib/Logic/Basic.lean | Ne.dite_ne_left_iff | [] | [
1193,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_reverse | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ darts (reverse p) = List.reverse (List.map Dart.symm (darts p))",
"tactic": "induction p <;> simp [*, Sym2.eq_swap]"
}
] | [
715,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_add' | [] | [
379,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.mem_of_mem_toEnumFinset | [] | [
131,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter_eq_nil | [] | [
176,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioo_mem_nhdsWithin_Iic | [] | [
570,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Algebra/Order/Kleene.lean | kstar_idem | [] | [
278,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Continuous.integrableOn_uIoc | [] | [
301,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_eq_equivFun | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : DecidableEq ι\nb : Basis ι R M\ninst✝ : Fintype ι\nm : M\ni : ι\n⊢ ↑(↑(toDual b) m) (↑b i) = ↑(equivFun b) m i",
"t... | [
350,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/Opposites.lean | AddOpposite.op_mul | [] | [
397,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousWithinAt_biInf | [] | [
1015,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/Data/List/Basic.lean | List.splitOnP.go_acc | [
{
"state_after": "no goals",
"state_before": "case nil\nι : Type ?u.293492\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nxs ys : List α\nls : List (List α)\nf : List α → List α\nacc : List α\n⊢ go p [] acc = modifyHead (fun x => reverse acc ++ x) (splitOnP p [])",
"tacti... | [
2931,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2923,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_b_eq_zero' | [] | [
336,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/Holor.lean | HolorIndex.cast_type | [
{
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63,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Analysis/Convex/Integral.lean | StrictConcaveOn.ae_eq_const_or_lt_map_average | [
{
"state_after": "no goals",
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324,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.toEquiv_injective | [] | [
58,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.nhds_of_ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.27734\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ✝ γ₁ γ₂ : Γ₀\nl : Filter α\nf : α → Γ₀\nγ : Γ₀\nh₀ : γ ≠ 0\n⊢ 𝓝 γ = pure γ",
"tactic": "rw [nhds_eq_update, update_noteq h₀]"
}
] | [
93,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_iInf | [
{
"state_after": "α : Type ?u.847795\nβ : Type ?u.847798\na b c✝ d : ℝ≥0∞\nr p q : ℝ≥0\nι : Sort u_1\nf g : ι → ℝ≥0∞\nc : ℝ≥0∞\n⊢ (a - ⨅ (i : ι), f i) ≤ c ↔ (⨆ (i : ι), a - f i) ≤ c",
"state_before": "α : Type ?u.847795\nβ : Type ?u.847798\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nι : Sort u_1\nf g : ι → ℝ≥0∞\n⊢ (a - ⨅... | [
2411,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2408,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_X_left_apply | [] | [
273,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_top | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.characteristic_iff_le_map | [
{
"state_after": "G : Type u_1\nG' : Type ?u.354562\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.354571\ninst✝ : AddGroup A\nH K : Subgroup G\n⊢ Characteristic H ↔ ∀ (ϕ : G ≃* G), H ≤ comap (MulEquiv.toMonoidHom (MulEquiv.symm ϕ)) H",
"state_before": "G : Type u_1\nG' : Type ?u.354562\ninst✝² : Group G... | [
2038,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2036,
1
] |
Mathlib/Data/List/Basic.lean | List.getI_eq_iget_get? | [
{
"state_after": "no goals",
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"tactic": "rw [← getD_default_eq_getI, getD_eq_getD_get?, Option.getD_def... | [
4499,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4498,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.of_subsingleton | [] | [
359,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.ae_lt_top' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1746227\nγ : Type ?u.1746230\nδ : Type ?u.1746233\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : AEMeasurable f\nh2f : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\n⊢ (∫⁻ (x : α), AEMeasurable.mk f hf x ∂μ) ≠ ⊤",
"tactic": "rwa [← lintegra... | [
1511,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Mathlib/Topology/Basic.lean | frontier_eq_closure_inter_closure | [
{
"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 α\n⊢ frontier s = closure s ∩ closure (sᶜ)",
"tactic": "rw [closure_compl, frontier, diff_eq]"
}
] | [
711,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfRightIso_π_app_left | [] | [
1710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
] |
src/lean/Init/Prelude.lean | isValidChar_UInt32 | [
{
"state_after": "no goals",
"state_before": "n : Nat\nh✝ : Nat.isValidChar n\nh : LT.lt n 55296\n⊢ LT.lt 55296 UInt32.size",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "n : Nat\nh✝ : Nat.isValidChar n\nleft✝ : LT.lt 57343 n\nh : LT.lt n 1114112\n⊢ LT.lt 1114112 UInt3... | [
2062,
48
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
2059,
9
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivWithinAt_snd | [] | [
269,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.inf_def | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_map_init_le | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
1298,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mem_inv_pointwise_smul_iff₀ | [] | [
460,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.erase_diff_erase_sublist | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl₁ l₂ : List α\nh : b :: l₁ <+ l₂\n⊢ List.diff (List.erase l₂ a) (List.erase (b :: l₁) a) <+ List.diff l₂ (b :: l₁)",
"tactic": "if heq : b = a then\n simp [heq]\nelse\n simp [heq, erase_comm a]\n exact (erase... | [
1553,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1545,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.symm_trans_apply | [] | [
393,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Complex/Module.lean | imaginaryPart_smul | [
{
"state_after": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\nz : ℂ\na : A\n⊢ ↑ℑ ((↑z.re + ↑z.im * I) • a) = z.re • ↑ℑ a + z.im • ↑ℜ a",
"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\nin... | [
507,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_min | [] | [
586,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_congr | [
{
"state_after": "case h\nα : Type u_1\nα' : Type ?u.28943\nβ : Type u_2\nβ' : Type ?u.28949\nγ : Type u_3\nγ' : Type ?u.28955\nδ : Type ?u.28958\nδ' : Type ?u.28961\nε : Type ?u.28964\nε' : Type ?u.28967\nζ : Type ?u.28970\nζ' : Type ?u.28973\nν : Type ?u.28976\nf f' : α → β → γ\ng g' : α → β → γ → δ\ns s' : S... | [
216,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.to_units_injective | [] | [
142,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_le_self | [] | [
341,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.widePushout_exists_rep' | [
{
"state_after": "case inl.intro\nC : Type u\ninst✝⁶ : Category C\ninst✝⁵ : ConcreteCategory C\nJ : Type v\ninst✝⁴ : SmallCategory J\nF : J ⥤ C\ninst✝³ : PreservesColimit F (forget C)\nB : C\nα : Type v\ninst✝² : Nonempty α\nX : α → C\nf : (j : α) → B ⟶ X j\ninst✝¹ : HasWidePushout B X f\ninst✝ : PreservesColim... | [
330,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.not_mem_of_not_mem_closure | [] | [
274,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_sub_cancel | [
{
"state_after": "n m : Nat\nthis : n + m - m = n\n⊢ n + m - m = n",
"state_before": "n m : Nat\nthis : n + m - (0 + m) = n\n⊢ n + m - m = n",
"tactic": "rw [Nat.zero_add] at this"
},
{
"state_after": "no goals",
"state_before": "n m : Nat\nthis : n + m - m = n\n⊢ n + m - m = n",
"tactic... | [
596,
46
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
594,
11
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.differentiableWithinAt | [] | [
112,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAtFilter_pi' | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type ?u.422469\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nG : Type ?u.422564\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : NormedSpace 𝕜 G\nG' : Type ?u... | [
398,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.comp_inv_eq_id | [] | [
494,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Topology/Order.lean | isOpen_sup | [] | [
681,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_inj | [] | [
240,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.mem_replaceF | [
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u_1\nβ : Type u_2\nk : α\nx : α × β\np : α × β → Bool\nf : α × β → β\n⊢ x ∈ List.replaceF (fun a => bif p a then some (k, f a) else none) [] → x.fst = k ∨ x ∈ []",
"tactic": "exact .inr"
},
{
"state_after": "case cons\nα : Type u_1... | [
201,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
189,
9
] |
Mathlib/FieldTheory/PerfectClosure.lean | MonoidHom.map_iterate_pthRoot | [] | [
111,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.coe_one | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.Paths.lift_cons | [] | [
86,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.dist_mem_uniformity | [] | [
816,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_neg_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.134372\nα : Type u_1\nβ : Type ?u.134378\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\n⊢ a / b < 0 ↔ 0 < a ∧ b < 0 ∨ a < 0 ∧ 0 < b",
"tactic": "simp [division_def, mul_neg_iff]"
}
] | [
685,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.wf_isOption | [
{
"state_after": "case moveLeft\nx✝¹ x : PGame\nIHl✝ : ∀ (i : LeftMoves x), Acc IsOption (moveLeft x i)\nIHr✝ : ∀ (j : RightMoves x), Acc IsOption (moveRight x j)\ny x✝ : PGame\ni : LeftMoves x✝\nIHl : ∀ (i : LeftMoves x✝), Acc IsOption (moveLeft x✝ i)\nIHr : ∀ (j : RightMoves x✝), Acc IsOption (moveRight x✝ j)... | [
242,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_add_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ sin (x + ↑π / 2) = cos x",
"tactic": "simp [sin_add]"
}
] | [
1279,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | geometric_hahn_banach_open_point | [] | [
122,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.nhds_infty_eq | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\n⊢ 𝓝 ∞ = map some (coclosedCompact X) ⊔ pure ∞",
"tactic": "rw [← nhdsWithin_compl_infty_eq, nhdsWithin_compl_singleton_sup_pure]"
}
] | [
334,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.expand_WF | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nsz : Nat\ninst✝¹ : BEq α\ninst✝ : Hashable α\nbuckets : Bucket α β\nH : Bucket.WF buckets\nx✝³ : AssocList α β\nx✝² : x✝³ ∈ (Bucket.mk (Array.size buckets.val * 2)).val.data\nx✝¹ : α × β\nx✝ : x✝¹ ∈ AssocList.toList x✝³\n⊢ (fun k x =>... | [
172,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
143,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yz_succ_succ | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ ↑(yn a1 (n + 2)) + ↑(yn a1 n) = ↑(2 * a) * ↑(yn a1 (n + 1))",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ yz a1 (n + 2) + yz a1 n = ↑(2 * a) * yz a1 (n + 1)",
"tactic": "delta yz"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < ... | [
544,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_mul_top | [] | [
561,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_of_nonpos | [
{
"state_after": "F : Type ?u.26833\nα : Type u_1\nβ : Type ?u.26839\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\nn : ℕ\nha : 0 ≤ 0\n⊢ ⌊0⌋₊ = 0",
"state_before": "F : Type ?u.26833\nα : Type u_1\nβ : Type ?u.26839\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\nha : ... | [
185,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | BoundedContinuousFunction.Lp_nnnorm_le | [
{
"state_after": "case hfC\nα : Type u_1\nE : Type u_2\nF : Type ?u.9383734\nG : Type ?u.9383737\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : TopologicalSpace α\ninst✝² : BorelSpac... | [
1613,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_symm_apply | [] | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq_lem1 | [
{
"state_after": "a : ℕ\na1 : 1 < a\ni n j : ℕ\nij : i < j + 1\njn : j + 1 < n\n⊢ xn a1 j % xn a1 n < xn a1 (j + 1) % xn a1 n",
"state_before": "a : ℕ\na1 : 1 < a\ni n j : ℕ\nij : i < j + 1\njn : j + 1 < n\n⊢ xn a1 i % xn a1 n < xn a1 (j + 1) % xn a1 n",
"tactic": "suffices xn a1 j % xn a1 n < xn a1 (j ... | [
656,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Algebra/Lie/Basic.lean | leibniz_lie | [] | [
136,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
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