file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.list_prod_subset_list_prod | [
{
"state_after": "case nil\nι : Type u_1\nα : Type u_2\nβ : Type ?u.71424\nF : Type ?u.71427\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : MonoidHomClass F α β\nt : List ι\nf₁ f₂ : ι → Set α\nhf✝ : ∀ (i : ι), i ∈ t → f₁ i ⊆ f₂ i\nhf : ∀ (i : ι), i ∈ [] → f₁ i ⊆ f₂ i\n⊢ List.prod (List.map f₁ []) ⊆ List... | [
117,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_add_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ : R[X]\nι : Type ?u.511565\np q : R[X]\n⊢ natDegree (p + q) ≤ max (natDegree p) (natDegree q)",
"tactic": "cases' le_max_iff.1 (degree_add_le p q) with h h <;> simp [natDegree_le_natDegr... | [
647,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.InitialMonoClass.of_isInitial | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nI : C\nhI : IsInitial I\nh : ∀ (X : C), Mono (IsInitial.to hI X)\nI' X : C\nhI' : IsInitial I'\n⊢ Mono (IsInitial.to hI' X)",
"state_before": "C : Type u₁\ninst✝ : Category C\nI : C\nhI : IsInitial I\nh : ∀ (X : C), Mono (IsInitial.to hI X)\nI' X : C\nhI' :... | [
529,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | sq_ne_one_iff | [] | [
267,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.image_inter_image_iff | [] | [
333,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_eq_algebra_adjoin | [] | [
436,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableAt_sub_const_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.503551\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
566,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/RingTheory/Valuation/Quotient.lean | Valuation.self_le_supp_comap | [
{
"state_after": "R : Type u_1\nΓ₀ : Type u_2\ninst✝¹ : CommRing R\ninst✝ : LinearOrderedCommMonoidWithZero Γ₀\nv✝ : Valuation R Γ₀\nJ : Ideal R\nv : Valuation (R ⧸ J) Γ₀\n⊢ Ideal.map (Ideal.Quotient.mk J) J ≤ supp v",
"state_before": "R : Type u_1\nΓ₀ : Type u_2\ninst✝¹ : CommRing R\ninst✝ : LinearOrderedC... | [
58,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.composition | [] | [
743,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_true | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/MeasureTheory/Covering/LiminfLimsup.lean | blimsup_cthickening_ae_le_of_eventually_mul_le_aux | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : MeasureTheory.Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nhs : ∀ (i : ℕ), IsClosed (s i)\nr₁ r₂ : ... | [
153,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.cons_injective2 | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nx y : α\ns t : Seq α\nh : cons x s = cons y t\n⊢ x = y",
"tactic": "rw [← Option.some_inj, ← get?_cons_zero, h, get?_cons_zero]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type... | [
109,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.sInf_eq_zero | [
{
"state_after": "no goals",
"state_before": "s : Set ℕ\n⊢ sInf s = 0 ↔ 0 ∈ s ∨ s = ∅",
"tactic": "cases eq_empty_or_nonempty s with\n| inl h => subst h\n simp only [or_true_iff, eq_self_iff_true, iff_true_iff, iInf, InfSet.sInf,\n mem_empty_iff_false, exists_false, dif_ne... | [
57,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_val | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.439\nβ : Type u\nα : Type v\nγ : Type w\ninst✝ : CommMonoid α\ns : Finset α\n⊢ Multiset.prod s.val = Finset.prod s id",
"tactic": "rw [Finset.prod, Multiset.map_id]"
}
] | [
77,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.coe_nnabs | [] | [
442,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Set/Function.lean | AntitoneOn.mono | [] | [
304,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_def | [] | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.subtypeDomain_neg | [] | [
1137,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Subsingleton.strictAntiOn | [] | [
2689,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2688,
11
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.partialProd_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.86974\ninst✝ : Monoid α\nn : ℕ\nf : Fin n → α\n⊢ partialProd f 0 = 1",
"tactic": "simp [partialProd]"
}
] | [
228,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.prev_reverse_eq_next | [] | [
848,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
8
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_eq_iSup_eapprox_lintegral | [
{
"state_after": "case e_f\nα : Type u_1\nβ : Type ?u.485014\nγ : Type ?u.485017\nδ : Type ?u.485020\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ (fun a => f a) = fun a => ⨆ (n : ℕ), ↑(eapprox f n) a",
"state_before": "α : Type u_1\nβ : Type ?u.485014\nγ : Type ?u.485017\nδ : ... | [
478,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | memℓp_zero_iff | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\n⊢ (if 0 = 0 then Set.Finite {i | ¬f i = 0}\n else if 0 = ⊤ then BddAbove (Set.range fun i => ‖f i‖) else Summable fun i => ‖f i‖ ^ 0) ↔\n Set.Finite {i | ¬f i = 0}",
"state_befo... | [
88,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Order/Minimal.lean | minimals_of_symm | [] | [
115,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.comp_apply | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.plusMap_toPlus | [
{
"state_after": "case w.h\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\nP : Cᵒᵖ ⥤ D\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nX : Cᵒᵖ\n⊢ (plusMap J (toPlus J P))... | [
276,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Order/Filter/Basic.lean | Set.MapsTo.tendsto | [] | [
3129,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3127,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.not_mem_iff | [
{
"state_after": "R : Type u\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nr : R\na : A\n⊢ ¬¬r ∈ σ a ↔ ¬IsUnit (↑↑ₐ r - a)",
"state_before": "R : Type u\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nr : R\na : A\n⊢ ¬r ∈ σ a ↔ IsUnit (↑↑ₐ r - a)",
... | [
114,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.pow_card_le_prod | [
{
"state_after": "ι : Type ?u.130494\nα : Type u_1\nβ : Type ?u.130500\nγ : Type ?u.130503\ninst✝ : OrderedCommMonoid α\ns t : Multiset α\na : α\nh : ∀ (x : α), x ∈ s → a ≤ x\n⊢ prod (map (Function.const α a) s) ≤ prod s",
"state_before": "ι : Type ?u.130494\nα : Type u_1\nβ : Type ?u.130500\nγ : Type ?u.13... | [
426,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Order/RelClasses.lean | IsStrictTotalOrder.swap | [] | [
233,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Set/Sups.lean | Set.Nonempty.of_sups_right | [] | [
128,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAdjointPair.comp | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_4\ninst✝²⁴ : Semiring R\ninst✝²³ : AddCommMonoid M\ninst✝²² : Module R M\nR₁ : Type ?u.1095252\nM₁ : Type ?u.1095255\ninst✝²¹ : Ring R₁\ninst✝²⁰ : AddCommGroup M₁\ninst✝¹⁹ : Module R₁ M₁\nR₂ : Type ?u.1095864\nM₂ : Type ?u.1095867\ninst✝... | [
1076,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_div' | [
{
"state_after": "case a\nR : Type u\ninst✝¹ : Semifield R\ninst✝ : StarRing R\nx y : R\n⊢ op (star (x / y)) = op (star x / star y)",
"state_before": "R : Type u\ninst✝¹ : Semifield R\ninst✝ : StarRing R\nx y : R\n⊢ star (x / y) = star x / star y",
"tactic": "apply op_injective"
},
{
"state_afte... | [
447,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.strictMono_subseq_of_tendsto_atTop | [] | [
593,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.isTorsion'_iff_torsion'_eq_top | [
{
"state_after": "R : Type u_3\nM : Type u_1\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nS : Type u_2\ninst✝² : CommMonoid S\ninst✝¹ : DistribMulAction S M\ninst✝ : SMulCommClass S R M\nh : torsion' R M S = ⊤\nx : M\n⊢ x ∈ ⊤",
"state_before": "R : Type u_3\nM : Type u_1\ninst✝⁵ ... | [
640,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.succ_eval | [
{
"state_after": "no goals",
"state_before": "⊢ eval succ = fun v => pure [Nat.succ (List.headI v)]",
"tactic": "simp [eval]"
}
] | [
146,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_coe' | [] | [
89,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_inv_cancel_left | [] | [
291,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
11
] |
Std/Data/Array/Lemmas.lean | Array.mapIdx_induction' | [] | [
207,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
203,
1
] |
Mathlib/Analysis/Convex/Side.lean | Sbtw.sOppSide_of_not_mem_of_mem | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.356013\nP : Type u_3\nP' : Type ?u.356019\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 y z : P\nh... | [
721,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.Lex.acc | [] | [
160,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_eq_nil_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.614\nε : Type ?u.617\nf : α → β → γ\nl : List α\nl' : List β\n⊢ zipWith f l l' = [] ↔ l = [] ∨ l' = []",
"tactic": "cases l <;> cases l' <;> simp"
}
] | [
55,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/PFun.lean | PFun.dom_toSubtype | [] | [
543,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_succ_iff_deriv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜... | [
2152,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2149,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_conjTranspose | [] | [
682,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_le | [] | [
113,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_empty_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns s₁ s₂ t t₁ t₂ u : Finset α\na b c : α\n⊢ s ○ ∅ = ∅",
"tactic": "simp [disjSups]"
}
] | [
494,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_lt_iff_lt_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ a / b < c ↔ a < b * c",
"tactic": "rw [div_lt_iff_lt_mul, mul_comm]"
}
] | [
986,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | eq_mul_inv_iff_mul_eq₀ | [] | [
36,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.coe_mrange | [] | [
1046,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.zpow_apply | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Data/List/Basic.lean | List.eq_replicate_length | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12121\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\n⊢ [] = replicate (length []) a ↔ ∀ (b : α), b ∈ [] → b = a",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12121\nα : Type u... | [
433,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.two_lt_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.58012\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ 2 < card s ↔ ∃ a, a ∈ s ∧ ∃ b, b ∈ s ∧ ∃ c, c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c",
"tactic": "simp_rw [two_lt_card_iff, exists_and_left]"
}
] | [
586,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Set/Function.lean | Set.LeftInvOn.surjOn | [] | [
1049,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.forall | [] | [
85,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_comp | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_le_iff_right | [] | [
623,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality | [
{
"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 X X' : C\nf : X ⟶ X'\n⊢ f ≫ (ρ_ X').inv = (ρ_ X).inv ≫ (f ⊗ 𝟙 tensorUnit')",
"tactic": "simp"
}
] | [
268,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.le_degree_of_mem_supp | [] | [
498,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.closure_induction'' | [] | [
106,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_contract_of_basis' | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁶ : CommRing R\nM : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nN : Type ?u.355819\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\nι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nb : Basis ι R M\n⊢ trace R M = comp (contrac... | [
158,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Group/Conj.lean | conj_injective | [] | [
128,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.inter_le_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.174218\nγ : Type ?u.174221\ninst✝ : DecidableEq α\ns✝¹ t✝ u : Multiset α\na✝ b : α\ns✝ : Multiset α\na : α\ns : Multiset α\nIH : ∀ (t : Multiset α), s ∩ t ≤ t\nt : Multiset α\nh : a ∈ t\n⊢ (a ::ₘ s) ∩ t ≤ t",
"tactic": "simpa [h] us... | [
1778,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1776,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_comp_le | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nX Y Z : C\nf✝ : X ⟶ Y\ninst✝² : HasImage f✝\nX' : C\nh : X' ⟶ X\nf : X ⟶ Y\ninst✝¹ : HasImage f\ninst✝ : HasImage (h ≫ f)\n⊢ image.preComp h f ≫ image.ι f = image.ι (h ≫ f)",
"tactic": "simp"
}
] | [
362,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieIdeal.map_comap_bracket_eq | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nf : L →ₗ⁅R⁆ L'\nI : LieIdeal R L\nJ J₁ J₂ : LieIdeal R L'\nh : LieHom.IsIdealMorphism f\n⊢ ⁅LieHom.idealRange f ⊓ J₁, LieHom.idealRange f ⊓ J₂⁆ ... | [
331,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.ext | [] | [
148,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.exists_prime_and_dvd | [
{
"state_after": "case intro\nn : ℕ+\nhn : n ≠ 1\np : ℕ\nhp : Nat.Prime p ∧ p ∣ ↑n\n⊢ ∃ p, Prime p ∧ p ∣ n",
"state_before": "n : ℕ+\nhn : n ≠ 1\n⊢ ∃ p, Prime p ∧ p ∣ n",
"tactic": "obtain ⟨p, hp⟩ := Nat.exists_prime_and_dvd (mt coe_eq_one_iff.mp hn)"
},
{
"state_after": "case intro\nn : ℕ+\nhn ... | [
155,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.preimage_of_open_map | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.25326\nπ : ι → Type ?u.25331\ninst✝¹ : TopologicalSpace α\ns✝ t u✝ v✝ : Set α\ninst✝ : TopologicalSpace β\ns : Set β\nhs : IsPreconnected s\nf : α → β\nhinj : Injective f\nhf : IsOpenMap f\nu v : Set α\nhu : IsOpen u\nhv : IsOpen v\nhsuv : f ⁻¹' s ⊆ u ∪ v\nh... | [
389,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.circleTransformDeriv_bound | [
{
"state_after": "case intro.intro\nE : Type ?u.227414\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR✝ : ℝ\nz✝ w : ℂ\nR : ℝ\nhR : 0 < R\nz x : ℂ\nf : ℂ → ℂ\nhx : x ∈ ball z R\nhf : ContinuousOn f (sphere z R)\nr : ℝ\nhr : r < R\nhrx : x ∈ ball z r\n⊢ ∃ B ε, 0 < ε ∧ ball x ε ⊆ ball z R ∧ ∀ (t : ℝ) (y... | [
177,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toLinearEquiv_apply | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.zero_shiftr | [] | [
457,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl✝ : Filter α\nk✝ f g g' : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nl : Filter α\nk : α → β\nz : ℕ\n⊢ Tendsto (fun a => k a ^ z * OfNat.ofNat 0 a) l (𝓝 0)",
"tactic": "simpa only [Pi.zero_apply, MulZeroClass.mu... | [
84,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.446238\nγ : Type ?u.446241\ninst✝ : DecidableEq α\ns✝ t✝ s t : Multiset α\n⊢ ∀ (a : α), a ∈ toFinset (s + t) ↔ a ∈ toFinset s ∪ toFinset t",
"tactic": "simp"
}
] | [
3158,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3157,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearMap.compPMap_apply | [] | [
651,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsTerminal.hasTerminal | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX : C\nh : IsTerminal X\nF : Discrete PEmpty ⥤ C\n⊢ (X_1 : Discrete PEmpty) → ((Functor.const (Discrete PEmpty)).obj X).obj X_1 ⟶ F.obj X_1",
"tactic": "aesop_cat"
},
{
"state_after": "no goals",
"state_before": "... | [
330,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.inf_neBot_iff | [] | [
679,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/RingTheory/Algebraic.lean | Algebra.IsAlgebraic.algHom_bijective | [
{
"state_after": "K : Type u_1\nL : Type u_2\nR : Type ?u.339073\nS : Type ?u.339076\nA : Type ?u.339079\ninst✝¹² : Field K\ninst✝¹¹ : Field L\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : CommRing A\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra L A\ninst✝⁵ : Algebra K A\ninst✝⁴ : IsScalarTower K L A\ninst✝³ :... | [
274,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_sub_add_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.133314\nβ : Type ?u.133317\nγ : Type ?u.133320\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\n⊢ a + b - (a + c) = b - c",
"tactic": "rw [← sub_sub, add_sub_cancel]"
}
] | [
609,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Topology/PathConnected.lean | Path.truncate_range | [
{
"state_after": "X✝ : Type ?u.458739\nY : Type ?u.458742\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.458757\nγ✝ : Path x y\nX : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\nt₀ t₁ : ℝ\n⊢ range ↑(truncate γ t₀ t₁) ⊆ range (extend γ)",
"state_before": "X... | [
664,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.zsmul_hom | [] | [
307,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_min | [] | [
111,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_val_succ' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.14497\nn' : Type ?u.14500\no' : Type ?u.14503\ni : ℕ\nh : Nat.succ i < Nat.succ m\nx : α\nu : Fin m → α\n⊢ vecCons x u { val := Nat.succ i, isLt := h } = u { val := i, isLt := (_ : i < m) }",
"tactic": "simp only [vecCons,... | [
144,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.face_eq_mkOfPoint | [
{
"state_after": "case h\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nn : ℕ\ns : Simplex k P n\ni : Fin (n + 1)\ni✝ : Fin (0 + 1)\n⊢ points (face s (_ : Finset.card {i} = 1)) i✝ = points (mkOfPoint k (points s i)) i✝",
"st... | [
858,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.arrow_intersect | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nS✝ R✝ : Sieve X\nJ : GrothendieckTopology C\nf : Y ⟶ X\nS R : Sieve X\nhS : Covers J S f\nhR : Covers J R f\n⊢ Covers J (S ⊓ R) f",
"tactic": "simpa [covers_iff] using And.intro hS hR"
}
] | [
218,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/NormedSpace/Int.lean | Int.norm_coe_units | [
{
"state_after": "no goals",
"state_before": "e : ℤˣ\n⊢ ‖↑e‖ = 1",
"tactic": "rw [← coe_nnnorm, nnnorm_coe_units, NNReal.coe_one]"
}
] | [
35,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_conj' | [] | [
618,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.div_mod_eq_mod_mul_div | [
{
"state_after": "no goals",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhb0 : b = 0\n⊢ a / b % c = a % (b * c) / b",
"tactic": "simp [hb0]"
},
{
"state_after": "no goals",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhb0 : ¬b = 0\n⊢ a / b % c = a % (b * c) / b",
"tactic": "rw [← @add_right... | [
416,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_add' | [] | [
720,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | Units.dvd_mul_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b : α\nu : αˣ\nx✝ : a ∣ b * ↑u\nc : α\nEq : b * ↑u = a * c\n⊢ b = a * (c * ↑u⁻¹)",
"tactic": "rw [← mul_assoc, ← Eq, Units.mul_inv_cancel_right]"
}
] | [
38,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : GroupWithZero α\na b : α\ninst✝² : Invertible a\ninst✝¹ : Invertible b\ninst✝ : Invertible (a / b)\n⊢ a / b * (b / a) = 1",
"tactic": "simp [← mul_div_assoc]"
}
] | [
420,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Restrict.lean | AffineMap.restrict.linear | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Topology/Separation.lean | Specializes.eq | [] | [
532,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_left_inv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_4\nE : Type u_3\nM : Type u_1\nH : Type u_2\nE' : Type ?u.133168\nM' : Type ?u.133171\nH' : Type ?u.133174\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : Topologic... | [
815,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.mem_powersetLen | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : ℕ\ns t : Multiset α\nl : List α\n⊢ s ∈ powersetLen n (Quotient.mk (isSetoid α) l) ↔ s ≤ Quotient.mk (isSetoid α) l ∧ ↑card s = n",
"tactic": "simp [powersetLen_coe']"
}
] | [
262,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.sq_mem_of_index_two | [] | [
217,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | WellFounded.rank_lt_of_rel | [] | [
2572,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2571,
1
] |
Mathlib/Data/Set/Prod.lean | Set.disjoint_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.14121\nδ : Type ?u.14124\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\n⊢ Disjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Disjoint s₁ s₂ ∨ Disjoint t₁ t₂",
"tactic": "simp_rw [disjoint_left, mem_prod, not_and_or, Prod.forall, and_i... | [
178,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.Factors.ramificationIdx_ne_zero | [] | [
711,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.comap_comp | [
{
"state_after": "case h.h\nX : Type u_2\nY : Type u_3\nZ : Type u_1\nα : Type u_4\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X → Y\ng : Y → Z\nhf : Continuous f\nhg : Continuous g\nx✝¹ : LocallyConstant Z α\nx✝ : X\n⊢ ↑((comap f ∘ comap g) x✝¹) x✝ = ↑(comap (g ∘ ... | [
493,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | AnalyticAt.differentiableWithinAt | [] | [
61,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.