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/List/Sublists.lean | List.sublists_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\n⊢ sublists (map f []) = map (map f) (sublists [])",
"tactic": "simp"
},
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\na : α\nl : List α\n⊢ (List.bind (List.bind (sublists l) fun x => [... | [
407,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.eq_sum_three_roots | [
{
"state_after": "R : Type ?u.935152\nS : Type ?u.935155\nF : Type u_1\nK : Type u_2\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : roots (map φ P) = {x, y, z}\n⊢ toPoly (map φ P) =\n toPoly\n { a := ↑φ P.a, b := ↑φ P.a * -(x + y + z), c := ↑φ P.a * (x * y + ... | [
539,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x (-y) = 0\nh0 : x ≠ 0\n⊢ angle x (x - y) < π / 2",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x ≠ 0\n⊢ angle x ... | [
277,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepFun.indepFun_finset | [
{
"state_after": "Ω : Type u_1\nι✝ : Type ?u.3366215\nβ✝ : Type ?u.3366218\nβ' : Type ?u.3366221\nγ : Type ?u.3366224\nγ' : Type ?u.3366227\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf✝ : Ω → β✝\ng : Ω → β'\ninst✝ : IsProbabilityMeasure μ\nι : Type u_2\nβ : ι → Type u_3\nm : (i : ι) → MeasurableSpace... | [
819,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_dvd_gcd_mul_left_right | [] | [
138,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
137,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.efixedPoint_eq_of_edist_lt_top' | [
{
"state_after": "case refine'_3\nα : Type u_1\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\nhf : ContractingWith K f\ns : Set α\nhsc : IsComplete s\nhsf : MapsTo f s s\nhfs : ContractingWith K (MapsTo.restrict f s s hsf)\nx : α\nhxs : x ∈ s\nhx : edist x (f x) ≠ ⊤\nt : Set α\nhtc : IsCompl... | [
258,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Logic/Basic.lean | forall_prop_of_false | [] | [
887,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_one | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.le_minDegree_of_forall_le_degree | [
{
"state_after": "case intro\nι : Sort ?u.291752\n𝕜 : Type ?u.291755\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w : V\ne : Sym2 V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Nonempty V\nk : ℕ\nh : ∀ (v : V), k ≤ degree G v\nv : V\nhv : minDegree G = deg... | [
1535,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Mathlib/Logic/Basic.lean | Xor'.or | [] | [
299,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.Limits.hasCoequalizer_of_common_section | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nA✝ B✝ : C\nf✝ g✝ : A✝ ⟶ B✝\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\ninst✝ : HasReflexiveCoequalizers C\nA B : C\nf g : A ⟶ B\nr : B ⟶ A\nrf : r ≫ f = 𝟙 B\nrg : r ≫ g = 𝟙 B\nthis : IsReflexivePair f g := IsReflexivePair.mk' r rf rg... | [
158,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_distrib_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_2\nγ : Type u_1\nδ : Type ?u.233403\nε : Type ?u.233406\nf : α → β → γ\nl : List α\nl' : List β\nn : ℕ\n⊢ tail (zipWith f l l') = zipWith f (tail l) (tail l')",
"tactic": "simp_rw [← drop_one, zipWith_distrib_drop]"
}
] | [
495,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.of_equiv | [] | [
296,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curryFinFinset_apply | [] | [
1861,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1858,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.indicator_summable | [
{
"state_after": "α : Type u_1\nβ : Type ?u.317811\nγ : Type ?u.317814\nf : α → ℝ≥0\nhf : Summable f\ns : Set α\na : α\n⊢ (if a ∈ s then f a else 0) ≤ f a",
"state_before": "α : Type u_1\nβ : Type ?u.317811\nγ : Type ?u.317814\nf : α → ℝ≥0\nhf : Summable f\ns : Set α\n⊢ Summable (indicator s f)",
"tacti... | [
1180,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_bit0' | [] | [
319,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.findMin'_all | [] | [
624,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_eq_one | [] | [
71,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.func_mem | [
{
"state_after": "case mk\nα✝ : Type u_1\nA✝ : α✝ → PSet\ni : Type (mk α✝ A✝)\n⊢ Func (mk α✝ A✝) i ∈ mk α✝ A✝",
"state_before": "x : PSet\ni : Type x\n⊢ Func x i ∈ x",
"tactic": "cases x"
},
{
"state_after": "no goals",
"state_before": "case mk\nα✝ : Type u_1\nA✝ : α✝ → PSet\ni : Type (mk α✝... | [
281,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Algebra/Bounds.lean | IsLUB.inv | [] | [
90,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Std/Data/List/Lemmas.lean | List.get_of_append | [
{
"state_after": "α : Type u_1\nl₁ : List α\na : α\nl₂ : List α\nn : Nat\nl : List α\neq : l = l₁ ++ a :: l₂\nh : length l₁ = n\n⊢ get? (a :: l₂) 0 = some a",
"state_before": "α : Type u_1\nl₁ : List α\na : α\nl₂ : List α\nn : Nat\nl : List α\neq : l = l₁ ++ a :: l₂\nh : length l₁ = n\n⊢ some (get l { val :... | [
614,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
612,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_one | [] | [
1047,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.multiset_prod_comp | [] | [
1143,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Real.rpow_eq_nhds_of_neg | [
{
"state_after": "p : ℝ × ℝ\nhp_fst : p.fst < 0\nthis : ∀ᶠ (x : ℝ × ℝ) in 𝓝 p, x.fst < 0\n⊢ (fun x => x.fst ^ x.snd) =ᶠ[𝓝 p] fun x => exp (log x.fst * x.snd) * cos (x.snd * π)\n\ncase this\np : ℝ × ℝ\nhp_fst : p.fst < 0\n⊢ ∀ᶠ (x : ℝ × ℝ) in 𝓝 p, x.fst < 0",
"state_before": "p : ℝ × ℝ\nhp_fst : p.fst < 0\... | [
209,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_range | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.90314\nπ : ι → Type ?u.90319\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\ninst✝ : CompactSpace α\nf : α → β\nhf : Continuous f\n⊢ IsCompact (f '' univ)",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.90314\nπ : ι → Type ... | [
848,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_bot | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.702130\nR : Type u_2\nA : Type u_1\nB : Type ?u.702139\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRin... | [
705,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Topology/PathConnected.lean | Path.source | [] | [
124,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_ofReal' | [] | [
192,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/FreeMonoid/Count.lean | FreeAddMonoid.count_of | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidableEq α\nx y : α\n⊢ ↑(count x) (of y) = Pi.single x 1 y",
"tactic": "simp [Pi.single, Function.update, count, countp, List.countp, List.countp.go,\n Bool.beq_eq_decide_eq]"
}
] | [
49,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/List/Basic.lean | List.isEmpty_iff_eq_nil | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.27737\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\n⊢ isEmpty l = true ↔ l = []",
"tactic": "cases l <;> simp [isEmpty]"
}
] | [
677,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_le_nhds | [
{
"state_after": "α : Type u_1\nβ : Type ?u.11749\nγ : Type ?u.11752\nδ : Type ?u.11755\ninst✝ : TopologicalSpace α\na : α\ns : Set α\n⊢ 𝓝[s] a ≤ 𝓝[univ] a",
"state_before": "α : Type u_1\nβ : Type ?u.11749\nγ : Type ?u.11752\nδ : Type ?u.11755\ninst✝ : TopologicalSpace α\na : α\ns : Set α\n⊢ 𝓝[s] a ≤ 𝓝... | [
208,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_eq_emptyset | [
{
"state_after": "case h\nR : Type ?u.1158991\nR' : Type ?u.1158994\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1159000\n𝕜₃ : Type ?u.1159003\n𝕝 : Type ?u.1159006\nE : Type u_2\nE₂ : Type ?u.1159012\nE₃ : Type ?u.1159015\nF : Type ?u.1159018\nG : Type ?u.1159021\nι : Type ?u.1159024\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : Ad... | [
919,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.one_mem_div | [] | [
1129,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | inv_mul_eq_iff_eq_mul₀ | [] | [
44,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_inf_le_inf_sSup | [] | [
1927,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1926,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.trans | [] | [
477,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.IsRoot.map | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf✝ f : R →+* S\nx : R\np : R[X]\nh : IsRoot p x\n⊢ IsRoot (Polynomial.map f p) (↑f x)",
"tactic": "rw [IsRoot, eval_map, eval₂_hom, h.eq_zero, ... | [
1200,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.lift_unique | [
{
"state_after": "C : Type u_3\ninst✝¹ : Category C\nr : HomRel C\nD : Type u_4\ninst✝ : Category D\nΦ : Quotient r ⥤ D\nH : ∀ (x y : C) (f₁ f₂ : x ⟶ y), r f₁ f₂ → (functor r ⋙ Φ).map f₁ = (functor r ⋙ Φ).map f₂\n⊢ Φ = lift r (functor r ⋙ Φ) H",
"state_before": "C : Type u_3\ninst✝¹ : Category C\nr : HomRel... | [
199,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.apply_eq_iff_eq_symm_apply | [] | [
871,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.add_mul | [
{
"state_after": "a b c : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\nn₃ : ℤ\nd₃ : ℕ\nh₃ : d₃ ≠ 0\n⊢ (n₁ * ↑d₂ + n₂ * ↑d₁) * n₃ /. (↑d₁ * ↑d₂ * ↑d₃) =\n (n₁ * n₃ * (↑d₂ * ↑d₃) + n₂ * n₃ * (↑d₁ * ↑d₃)) /. (↑d₁ * ↑d₃ * (↑d₂ * ↑d₃))",
"state_before": "a b c : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\... | [
278,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
11
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_zero | [] | [
372,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean | Euclidean.closure_ball | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : TopologicalAddGroup E\ninst✝³ : T2Space E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : FiniteDimensional ℝ E\nx : E\nr : ℝ\nh : r ≠ 0\n⊢ closure (ball x r) = closedBall x ... | [
101,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
8
] |
Mathlib/Data/Subtype.lean | Subtype.prop | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Data/List/Basic.lean | List.some_nthLe_eq | [] | [
1498,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1497,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_succAbove | [
{
"state_after": "case inl\nn : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : ↑castSucc j < i\n⊢ ↑(cycleRange i) (↑(succAbove i) j) = succ j\n\ncase inr\nn : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : ↑castSucc j ≥ i\n⊢ ↑(cycleRange i) (↑(succAbove i) j) = succ j",
"state_before": "n : ℕ\ni : Fin (n + 1)\nj : Fin n\n⊢ ↑(cycle... | [
281,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.induce_empty | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.260256\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' G'' : Subgraph G\ns s' : Set V\n⊢ induce G' ∅ = ⊥",
"tactic": "ext <;> simp"
}
] | [
1170,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1169,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.not | [] | [
271,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.range_toContinuousMap | [
{
"state_after": "case h\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nv : PicardLindelof E\nf✝ : FunSpace v\nf : C(↑(Icc v.tMin v.tMax), E)\n⊢ f ∈ range ↑toContinuousMap ↔ f ∈ {f | ↑f v.t₀ = v.x₀ ∧ LipschitzWith v.C ↑f}",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E... | [
205,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.equiv_refl | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.474547\nM : Type ?u.474550\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' P Q : Submodule R M\nhf : map (↑(LinearEquiv.refl R M)) P = Q\n⊢ P = Q",
"tactic": "simpa using hf"
}
] | [
663,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.le_insertNth_iff | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ninst✝ : (i : Fin (n + 1)) → Preorder (α i)\ni : Fin (n + 1)\nx : α i\np : (j : Fin n) → α (↑(succAbove i) j)\nq : (j : Fin (n + 1)) → α j\n⊢ q ≤ insertNth i x p ↔ q i ≤ x ∧ (fun j => q (↑(succAbove i) j)) ≤ p",
... | [
809,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | vecCons2 | [] | [
96,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
9
] |
Mathlib/Logic/Function/Basic.lean | Function.leftInverse_iff_comp | [] | [
332,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_le_coe | [] | [
393,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_mem_vsub | [] | [
1464,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.coe_mk | [] | [
67,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
src/lean/Init/SizeOf.lean | Lean.Name.anonymous.sizeOf_spec | [] | [
103,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
102,
9
] |
Mathlib/Order/Heyting/Hom.lean | BiheytingHom.ext | [] | [
522,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atBot_mul_atBot | [
{
"state_after": "ι : Type ?u.198322\nι' : Type ?u.198325\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.198334\ninst✝ : StrictOrderedRing α\nl : Filter β\nf g : β → α\nhf : Tendsto f l atBot\nhg : Tendsto g l atBot\nthis : Tendsto (fun x => -f x * -g x) l atTop\n⊢ Tendsto (fun x => f x * g x) l atTop",
"state_be... | [
923,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.pow | [] | [
1460,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
8
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.1050897\nF : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns✝ : Set E\nf✝ : E → E\nf'✝ : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ :... | [
1245,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.mem_submoduleImage | [
{
"state_after": "case refine'_1\nR : Type u_2\nR₁ : Type ?u.1587077\nR₂ : Type ?u.1587080\nR₃ : Type ?u.1587083\nR₄ : Type ?u.1587086\nS : Type ?u.1587089\nK : Type ?u.1587092\nK₂ : Type ?u.1587095\nM : Type u_3\nM'✝ : Type ?u.1587101\nM₁ : Type ?u.1587104\nM₂ : Type ?u.1587107\nM₃ : Type ?u.1587110\nM₄ : Type... | [
1742,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1735,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.mem_ker | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ :... | [
958,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
Mathlib/Data/List/Basic.lean | List.surjective_head | [] | [
863,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.IsSymmetric.map | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\nτ : Type ?u.44691\nS : Type u_3\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nφ ψ : MvPolynomial σ R\nhφ : IsSymmetric φ\nf : R →+* S\ne : Perm σ\n⊢ ↑(rename ↑e) (↑(MvPolynomial.map f) φ) = ↑(MvPolynomial.map f) φ",
"tactic": ... | [
137,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.exists_aleph | [
{
"state_after": "c : Cardinal\nh : ℵ₀ ≤ c\n⊢ ω ≤ alephIdx c",
"state_before": "c : Cardinal\nh : ℵ₀ ≤ c\n⊢ c = aleph (alephIdx c - ω)",
"tactic": "rw [aleph, Ordinal.add_sub_cancel_of_le, aleph'_alephIdx]"
},
{
"state_after": "no goals",
"state_before": "c : Cardinal\nh : ℵ₀ ≤ c\n⊢ ω ≤ alep... | [
331,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.mulInitial_inv | [] | [
143,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.measurable | [] | [
1054,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.map_mono | [] | [
136,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.sound | [] | [
697,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.pow_eq_pow_iff | [
{
"state_after": "case intro\nι : Type ?u.1415307\nα : Type ?u.1415310\nβ : Type u_1\nf✝ g : Perm α\nx y : α\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\ninst✝ : Finite β\nf : Perm β\nhf : IsCycle f\na b : ℕ\nval✝ : Fintype β\n⊢ f ^ a = f ^ b ↔ ∃ x, ↑f x ≠ x ∧ ↑(f ^ a) x = ↑(f ^ b) x",
"state_before": "ι : ... | [
724,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | MonoidHom.map_dfinsupp_prod | [] | [
2249,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2247,
1
] |
src/lean/Init/Data/Array/Mem.lean | Array.sizeOf_get_lt | [
{
"state_after": "case mk\nα : Type u_1\ninst✝ : SizeOf α\ndata✝ : List α\ni : Fin (size { data := data✝ })\n⊢ sizeOf (get { data := data✝ } i) < sizeOf { data := data✝ }",
"state_before": "α : Type u_1\ninst✝ : SizeOf α\nas : Array α\ni : Fin (size as)\n⊢ sizeOf (get as i) < sizeOf as",
"tactic": "case... | [
30,
40
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
26,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.pred_eq_iff_not_succ' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.82530\nβ : Type ?u.82533\nγ : Type ?u.82536\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ pred o = o ↔ ∀ (a : Ordinal), o ≠ succ a",
"tactic": "simpa using pred_eq_iff_not_succ"
}
] | [
190,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_quotient_le | [] | [
1970,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1969,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.exists_of_lt | [] | [
215,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Matrix/Hadamard.lean | Matrix.hadamard_zero | [] | [
106,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/PFilter.lean | Order.IsPFilter.of_def | [] | [
64,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Order/Bounds/Basic.lean | Antitone.map_bddBelow | [] | [
1332,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Nat.cast_list_sum | [] | [
2190,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2189,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupNorm.coe_lt_coe | [] | [
945,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/Computability/Primrec.lean | list_foldl' | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nσ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nH : Nat.Primrec fun n => encode (decode n)\nf : α → List β\ng : α → σ\nh : α → σ × β → σ\nhf : Primrec f\nhg : Primrec g\nhh : Primrec₂ h\nthis : Primcodable (List β) := prim H\n⊢ P... | [
918,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.IsProbabilityMeasure.ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.652108\nγ : Type ?u.652111\nδ : Type ?u.652114\nι : Type ?u.652117\nR : Type ?u.652120\nR' : Type ?u.652123\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Se... | [
3208,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3207,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.pullback_obj_left | [] | [
236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_le_add_right' | [
{
"state_after": "case refine'_1.inl\nxl xr : Type u_1\nxL : xl → PGame\nxR : xr → PGame\nyl yr : Type u_1\nyL : yl → PGame\nyR : yr → PGame\nzl zr : Type u_1\nzL : zl → PGame\nzR : zr → PGame\nh : mk xl xr xL xR ≤ mk yl yr yL yR\ni : xl\n⊢ (∃ i', moveLeft (mk xl xr xL xR + mk zl zr zL zR) (Sum.inl i) ≤ moveLef... | [
1724,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1705,
9
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.map_hom_map_inv_apply | [] | [
176,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_le_iff_eq_top | [] | [
528,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_iff_norm | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nι : Type u_2\nE : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : SeminormedAddCommGroup E\nl : Filter ι\nf : ι → α → E\ng : α → E\n⊢ TendstoInMeasure μ f l g ↔ ∀ (ε : ℝ), 0 < ε → Tendsto (fun i => ↑↑μ {x | ε ≤ ‖f i x - g x‖}) l (𝓝 0)",
... | [
65,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.BoundedFormula.listEncode_sigma_injective | [] | [
311,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.le_pushforward_pullback | [] | [
524,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Topology/Category/Compactum.lean | Compactum.le_nhds_of_str_eq | [
{
"state_after": "no goals",
"state_before": "X : Compactum\nF : Ultrafilter X.A\nx : X.A\nh : str X F = x\ns : Set X.A\nhx : x ∈ s\nhs : IsOpen s\n⊢ str X F ∈ s",
"tactic": "rwa [h]"
}
] | [
362,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.compactOpen_eq_compactConvergence | [
{
"state_after": "α : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\n⊢ TopologicalSpace.generateFrom {m | ∃ s x u x, m = CompactOpen.gen s u} =\n TopologicalSpace.mkOfNhds fun f => FilterBasis.filter (compactConvergenceFilterBasis f)",
... | [
289,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.233047\nι : Type ?u.233050\ninst✝² : Countable ι\nf g : α → β\ninst✝¹ : SeminormedAddCommGroup β\nm m0 : MeasurableSpace α\nhm : m ≤ m0\nhf : StronglyMeasurable f\nμ : Measure α\ninst✝ : SigmaFinite (trim μ hm)\nsigma_finite_sets : ℕ → Set α := spanningS... | [
977,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_mul_negOfNat | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ -[m+1] * negOfNat n = ofNat (succ m * n)",
"tactic": "cases n <;> rfl"
}
] | [
389,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
388,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.isProper_of_ne_top | [] | [
221,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_smul_le | [] | [
701,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | hasFPowerSeriesAt_iff' | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2404405\nG : Type ?u.2404408\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMul... | [
1420,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_assoc | [] | [
1401,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.cancel_right | [] | [
1162,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.op_norm_zero | [
{
"state_after": "no goals",
"state_before": "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)... | [
387,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Complex/Exponential.lean | isCauSeq_geo_series_const | [
{
"state_after": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : Archimedean α\na x : α\nhx1 : abs' x < 1\nthis : IsCauSeq abs' fun m => a * ∑ n in range m, x ^ n\n⊢ IsCauSeq abs' fun m => ∑ n in range m, a * x ^ n",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : Archimedean α\n... | [
156,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.