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 |
|---|---|---|---|---|---|---|
Std/Logic.lean | or_imp | [] | [
338,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
337,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.compl_not_mem | [] | [
704,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Init/Classical.lean | Classical.cases_true_false | [] | [
26,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
17
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.lsum_single | [
{
"state_after": "no goals",
"state_before": "ι : Type u_5\nR : Type u_3\nS : Type u_1\nM : ι → Type u_4\nN : Type u_2\ndec_ι : DecidableEq ι\ninst✝⁷ : Semiring R\ninst✝⁶ : (i : ι) → AddCommMonoid (M i)\ninst✝⁵ : (i : ι) → Module R (M i)\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\ninst✝² : Semiring S\ni... | [
173,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nndist_set_exists | [] | [
241,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | IsSelfAdjoint.exp | [] | [
147,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.comp_monotoneOn_right | [] | [
374,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.pow_lt_ascFactorial | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 2 ≤ 0 → (n + 1) ^ 0 < ascFactorial n 0",
"tactic": "rintro ⟨⟩"
},
{
"state_after": "n : ℕ\na✝ : 2 ≤ 1\n⊢ (n + 1) ^ 1 < ascFactorial n 1",
"state_before": "n : ℕ\n⊢ 2 ≤ 1 → (n + 1) ^ 1 < ascFactorial n 1",
"tactic": "intro"
},
{
... | [
302,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSet.iIndepFun_indicator | [
{
"state_after": "Ω : Type u_2\nι : Type u_3\nβ : Type u_1\nβ' : Type ?u.3674153\nγ : Type ?u.3674156\nγ' : Type ?u.3674159\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf : Ω → β\ng : Ω → β'\ninst✝¹ : Zero β\ninst✝ : One β\nm : MeasurableSpace β\ns : ι → Set Ω\nhs : iIndepSet s\n⊢ ∀ (S : Finset ι) {set... | [
917,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith3_same_left | [] | [
320,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/List/Basic.lean | List.splitOnP.go_ne_nil | [
{
"state_after": "case cons\nι : Type ?u.292233\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\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : ∀ (acc : List α), go p tail✝ acc ≠ []\nacc : List α\n⊢ ¬(if p head✝ = true then reverse ac... | [
2921,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2920,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.le_prod_of_submultiplicative | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.144665\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.144674\ninst✝¹ : CommMonoid α\ninst✝ : OrderedCommMonoid β\nf : α → β\nh_one : f 1 = 1\nh_mul : ∀ (a b : α), f (a * b) ≤ f a * f b\ns : Multiset α\n⊢ ∀ (a b : α), (fun x => True) a → (fun x => True) b →... | [
483,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.add_oreDiv | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nr r' : R\ns : { x // x ∈ S }\n⊢ r /ₒ s + r' /ₒ s = (r + r') /ₒ s",
"tactic": "simp [oreDiv_add_char s s 1 1 (by simp)]"
},
{
"state_after": "no goals",
"state_before": "R : Typ... | [
627,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_left_inj | [] | [
267,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_vecCons_smul | [] | [
835,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | lt_norm_sub_of_not_sameRay | [
{
"state_after": "𝕜 : Type ?u.62097\nE : Type u_1\ninst✝⁴ : NormedLinearOrderedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : StrictConvexSpace ℝ E\nx y z : E\na b r : ℝ\nh : ¬SameRay ℝ (x - y + y) y\n⊢ ‖x - y + y‖ - ‖y‖ < ‖x - y‖",
"state_before": "𝕜... | [
199,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_finsupp_of_infinite' | [
{
"state_after": "no goals",
"state_before": "α β : Type u\ninst✝² : Nonempty α\ninst✝¹ : Zero β\ninst✝ : Infinite β\n⊢ (#α →₀ β) = max (#α) (#β)",
"tactic": "simp"
}
] | [
1065,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.comp_apply | [] | [
412,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.start_isSpecial | [
{
"state_after": "no goals",
"state_before": "u : XgcdType\na b : ℕ+\n⊢ IsSpecial (start a b)",
"tactic": "dsimp [start, IsSpecial]"
}
] | [
262,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Order/Atoms.lean | OrderIso.isAtomic_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : OrderBot α\ninst✝ : OrderBot β\nf : α ≃o β\n⊢ IsAtomic α ↔ IsAtomic β",
"tactic": "simp only [IsAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff... | [
829,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
11
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.IsSplitEpi.mk' | [] | [
100,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.quotientInfToPiQuotient_bijective | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\nI : Ideal R\na b : R\nS ι : Type v\ninst✝ : Finite ι\nf : ι → Ideal R\nhf : ∀ (i j : ι), i ≠ j → f i ⊔ f j = ⊤\nx y : R ⧸ ⨅ (i : ι), f i\nr s : R\nhrs : ↑(quotientInfToPiQuotient f) (Quotient.mk'' r) = ↑(quotientInfToPiQuotient f) (Quotient.mk'' s)\ni : ι\n⊢ ↑(... | [
491,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_zpow | [] | [
280,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_cons | [] | [
132,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Std/Data/RBMap/Basic.lean | Std.RBNode.All.imp | [] | [
170,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
168,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_mono | [] | [
1432,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1431,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min_mono | [] | [
1301,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitUpper_le | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : Type ?u.12887\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ ↑(splitUpper I i x) ⊆ ↑↑I",
"tactic": "simp"
}
] | [
117,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Std/Data/Int/DivMod.lean | Int.ofNat_div | [] | [
19,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
19,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.of_prim | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nf : Vector ℕ n → ℕ\nthis : ∀ (f : ℕ → ℕ), Nat.Primrec f → Primrec' fun v => f (Vector.head v)\nhf : Primrec f\ni : Vector ℕ n\n⊢ Nat.pred ((fun m => encode (Option.map f (decode m))) (encode i)) = f i",
"tactic": "simp [encodek]"
},
{
"state_a... | [
1542,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1524,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.get?_of_eq_some_of_succ_get?_intFractPair_stream | [
{
"state_after": "K : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nifp_succ_n : IntFractPair K\nstream_succ_nth_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n\n⊢ Stream'.Seq.get?\n (match\n (IntFractPair.of v,\n Stream'.Seq.tail\n { val ... | [
247,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubmodule.normalizer_inf | [
{
"state_after": "case h\nR : Type u_2\nL : Type u_3\nM : Type u_1\nM' : Type ?u.11866\ninst✝¹⁰ : CommRing R\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 : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : ... | [
74,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.incidenceSet_subset_incidenceSet | [] | [
262,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Control/Traversable/Instances.lean | List.mem_traverse | [
{
"state_after": "no goals",
"state_before": "F G : Type u → Type u\ninst✝² : Applicative F\ninst✝¹ : Applicative G\nα' β' : Type u\nf✝ : α' → F β'\ninst✝ : LawfulApplicative F\nf : α' → Set β'\n⊢ [] ∈ traverse f [] ↔ Forall₂ (fun b a => b ∈ f a) [] []",
"tactic": "simp"
},
{
"state_after": "no ... | [
141,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MonotoneOn.const_mul' | [] | [
1295,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.empty_orelse | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation α\n⊢ IsBisimulation fun c₁ c₂ => (HOrElse.hOrElse (empty α) fun x => c₂) = c₁",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation α\n⊢ (HOrElse.hOrElse (empty α) fun x => c) = c",
"tactic": "apply eq_of_bisim (fun c... | [
966,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_iSup' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.480111\nγ : Type ?u.480114\nδ : Type ?u.480117\nm : MeasurableSpace α\nμ ν : Measure α\nf : ℕ → α → ℝ≥0∞\nhf : ∀ (n : ℕ), AEMeasurable (f n)\nh_mono : ∀ᵐ (x : α) ∂μ, Monotone fun n => f n x\n⊢ (∫⁻ (a : α), iSup (fun i => f i) a ∂μ) = ⨆ (n : ℕ), ∫⁻ (a : α), f n a ∂μ",
... | [
447,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Order/Filter/IndicatorFunction.lean | indicator_union_eventuallyEq | [] | [
48,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Order/Chain.lean | IsMaxChain.isChain | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.coe_le_coe | [] | [
547,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.isRight_eq_false | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.7480\nδ : Type ?u.7483\nx y : α ⊕ β\n⊢ isRight x = false ↔ isLeft x = true",
"tactic": "cases x <;> simp"
}
] | [
141,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | IsScalarTower.algebraMap_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\ninst✝² : SMul R M\ninst✝¹ : MulAction A M\ninst✝ : IsScalarTower R A M\nr : R\nx : M\n⊢ ↑(algebraMap R A) r • x = r • x",
"tacti... | [
73,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.one_comp | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.y_dvd_iff | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : yn a1 m ∣ yn a1 n\nhp : n % m > 0\nco : coprime (yn a1 m) (xn a1 (m * (n / m)))\n⊢ False",
"state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : yn a1 m ∣ yn a1 n\nhp : n % m > 0\n⊢ False",
"tactic": "have co : Nat.coprime (yn a1 m) (xn a1 (m * (n / m))) :=\n... | [
454,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Order/MinMax.lean | min_le_min | [] | [
80,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.basicOpen_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\n⊢ ↑(basicOpen 𝒜 1) = ↑⊤",
"tactic": "simp"
}
] | [
414,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.NatTrans.leftOp_comp | [] | [
398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/Holor.lean | Holor.mul_scalar_mul | [
{
"state_after": "no goals",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝ : Monoid α\nx : Holor α []\ny : Holor α ds\n⊢ x ⊗ y = x { val := [], property := (_ : Forall₂ (fun x x_1 => x < x_1) [] []) } • y",
"tactic": "simp [mul, SMul.smul, HolorIndex.take, HolorIndex.drop, HSMul.hSMul... | [
231,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.eq_inv_iff_mul_eq_one | [] | [
2174,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift | [
{
"state_after": "C : 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)\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nhQ : Presheaf.IsSheaf J Q\n⊢ (to... | [
565,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.mul_mem_centralizer | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nS T : Set M\na b : M\ninst✝ : Semigroup M\nha : a ∈ centralizer S\nhb : b ∈ centralizer S\ng : M\nhg : g ∈ S\n⊢ g * (a * b) = a * b * g",
"tactic": "rw [mul_assoc, ← hb g hg, ← mul_assoc, ha g hg, mul_assoc]"
}
] | [
76,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | archimedean_iff_rat_le | [] | [
373,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.infty_coeFn_nat_cast | [] | [
911,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.eq_bot_iff | [] | [
424,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.top_of_top_mem | [
{
"state_after": "case a.h\nP : Type u_1\ninst✝¹ : LE P\ninst✝ : OrderTop P\nI : Ideal P\nh : ⊤ ∈ I\nx✝ : P\n⊢ x✝ ∈ ↑I ↔ x✝ ∈ ↑⊤",
"state_before": "P : Type u_1\ninst✝¹ : LE P\ninst✝ : OrderTop P\nI : Ideal P\nh : ⊤ ∈ I\n⊢ I = ⊤",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before... | [
271,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.restrict_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝⁴ : MeasurableSpace Ω\nR : Type ?u.40459\ninst✝³ : SMul R ℝ≥0\ninst✝² : SMul R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nμ : FiniteMeasure Ω\nA : Set Ω\n⊢ restrict μ A = 0 ↔ (fun s => ENNReal.toNNReal (↑↑↑μ s)... | [
301,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_le_snorm'_mul_rpow_measure_univ | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.3186605\nG : Type ?u.3186608\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq✝ : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np q : ℝ\nhp0_lt : 0 < p\nhpq : p ≤ q\nf : α → E\nhf : AEStronglyMeasur... | [
1053,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.3235\nf✝ g✝ : Ultrafilter α\ns t : Set α\np q : α → Prop\nf : Filter α\nh₁ : NeBot f\nh₂ : ∀ (g : Filter α), NeBot g → g ≤ f → f ≤ g\ng : Filter α\nneBot'✝ : NeBot g\nle_of_le✝ : ∀ (g_1 : Filter α), NeBot g_1 → g_1 ≤ g → g ≤ g... | [
83,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toMonoidHom_commutes | [] | [
724,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.mem_jacobson_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI : Ideal R\nx : R\nhx : x ∈ jacobson ⊥\ny z : R\nhz : z * y * x + z - 1 ∈ ⊥\n⊢ (x * y + 1) * z = 1",
"tactic": "rwa [add_mul, one_mul, ← sub_eq_zero, mul_right_comm, mul_comm _ z, mul_right_co... | [
269,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | RingHom.asBoolAlg_comp | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.coprod_inl | [
{
"state_after": "case h\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.62156\nM₆ : Type ?u.62159\nS : Type ?u.62162\ninst✝¹³ : Semiring R\ninst✝¹² : Semiring S\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M₂\... | [
225,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.forkOfKernelFork_ι | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.ofNat'_succ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.180035\n⊢ ofNat' (0 + 1) = ofNat' 0 + 1",
"tactic": "simp"
},
{
"state_after": "case false\nα : Type ?u.180035\nn : ℕ\nih : ofNat' (n + 1) = ofNat' n + 1\n⊢ ofNat' (Nat.bit false n + 1) = ofNat' (Nat.bit false n) + 1\n\ncase true\nα : Typ... | [
263,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Matrix.det_comm' | [
{
"state_after": "R : Type ?u.22368\ninst✝¹¹ : CommRing R\nM✝ : Type ?u.22374\ninst✝¹⁰ : AddCommGroup M✝\ninst✝⁹ : Module R M✝\nM'✝ : Type ?u.22959\ninst✝⁸ : AddCommGroup M'✝\ninst✝⁷ : Module R M'✝\nι : Type ?u.23501\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ne : Basis ι R M✝\nA : Type u_3\ninst✝⁴ : CommRing ... | [
95,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.IsInvertedBy.rightOp | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u_2\ninst✝ : Category D\nW : MorphismProperty C\nL : Cᵒᵖ ⥤ D\nh : IsInvertedBy (MorphismProperty.op W) L\nX Y : C\nf : X ⟶ Y\nhf : W f\nthis : IsIso (L.map f.op)\n⊢ IsIso (L.rightOp.map f)",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Typ... | [
321,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Algebra/Order/Monoid/Defs.lean | add_top | [] | [
132,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nn : ℕ\nhn : ∀ (a : ℕ), a ∈ {n | map f ⊥ ≤ P ^ n} → a ≤ n\n⊢ Nat.succ n ∈ {n | map f ⊥ ≤ P ^ n}",
"tactic": "simp"
}
] | [
114,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.NeBot.prod | [] | [
440,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | mem_subalgebraOfSubring | [] | [
1505,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Submodule.coe_toSubalgebra | [] | [
568,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | ae_essInf_le | [] | [
126,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/GroupTheory/Commensurable.lean | Commensurable.commensurator'_mem_iff | [] | [
107,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.IsVanKampenColimit.of_map | [
{
"state_after": "J : Type v'\ninst✝⁷ : Category J\nC : Type u\ninst✝⁶ : Category C\nX Y : C\nD✝ : Type u''\ninst✝⁵ : Category D✝\nD : Type u_1\ninst✝⁴ : Category D\nG : C ⥤ D\nF : J ⥤ C\nc : Cocone F\ninst✝³ : PreservesLimitsOfShape WalkingCospan G\ninst✝² : ReflectsLimitsOfShape WalkingCospan G\ninst✝¹ : Pres... | [
544,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.evalList_sort_congr | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na b c : List Nat\nctx : Context α\nh : IsCommutative ctx.op\nh₂ : evalList α ctx a = evalList α ctx b\nh₃ : a ≠ []\nh₄ : b ≠ []\n⊢ evalList α ctx (sort.loop a c) = evalList α ctx (sort.loop b c)",
"tactic": "induction c generalizing a b with\n|... | [
208,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
191,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_of_nonpos | [] | [
929,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.lift_symm_apply | [] | [
246,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.coe_nat_succ_pos | [] | [
48,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.disjoint | [] | [
170,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
11
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.lift_word_prod_nontrivial_of_not_empty | [
{
"state_after": "case inl\nι : Type u_1\nM : ι → Type ?u.842716\ninst✝⁴ : (i : ι) → Monoid (M i)\nN : Type ?u.842727\ninst✝³ : Monoid N\nhnontriv : Nontrivial ι\nG : Type u_3\ninst✝² : Group G\nH : ι → Type u_2\ninst✝¹ : (i : ι) → Group (H i)\nf : (i : ι) → H i →* G\nα : Type ?u.843508\ninst✝ : MulAction G α\n... | [
803,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Data/Set/Basic.lean | MonotoneOn.union | [] | [
2914,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2912,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.X_add_C_ne_zero | [] | [
1392,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.not_neBot | [] | [
501,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
9
] |
Mathlib/Topology/Constructions.lean | inducing_iInf_to_pi | [] | [
1424,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_empty | [
{
"state_after": "case intro\nι : Sort ?u.54858\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx✝ y : α\ns t u : Set α\nΦ : α → β\nx : α\nxs : x ∈ s\n⊢ hausdorffEdist s ∅ = ⊤",
"state_before": "ι : Sort ?u.54858\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ni... | [
426,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_single_of_ne | [] | [
175,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.prod_snd | [] | [
244,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
11
] |
Mathlib/Algebra/Order/Module.lean | BddBelow.smul_of_nonpos | [] | [
214,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_subset_right | [] | [
234,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.eqv | [] | [
78,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.sqrt_eq_rpow | [
{
"state_after": "case inl\nz x✝ y x : ℝ\nh : 0 ≤ x\n⊢ sqrt x = x ^ (1 / 2)\n\ncase inr\nz x✝ y x : ℝ\nh : x < 0\n⊢ sqrt x = x ^ (1 / 2)",
"state_before": "z x✝ y x : ℝ\n⊢ sqrt x = x ^ (1 / 2)",
"tactic": "obtain h | h := le_or_lt 0 x"
},
{
"state_after": "case inl\nz x✝ y x : ℝ\nh : 0 ≤ x\n⊢ x ... | [
657,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Control/Traversable/Lemmas.lean | Traversable.map_traverse | [
{
"state_after": "t : Type u → Type u\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nα β γ : Type u\ng : α → F β\nh : β → G γ\nf : β → γ\nx✝ : t β\nx : t α\n⊢ traverse (pur... | [
84,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sdiff_sdiff_le_sdiff | [
{
"state_after": "ι : Type ?u.94869\nα : Type u_1\nβ : Type ?u.94875\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a ≤ a ⊔ (b ⊔ c)",
"state_before": "ι : Type ?u.94869\nα : Type u_1\nβ : Type ?u.94875\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ (a \\ b) \\ (a \\ c) ≤ c \\ b",
"tactic... | [
612,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_le_iff | [] | [
351,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.right_half_plane_of_tendsto_zero_on_real | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b C : ℝ\nf g : ℂ → E\nhd : DiffContOnCl ℂ f {z | 0 < z.re}\nhexp : ∃ c, c < 2 ∧ ∃ B, f =O[comap (↑Complex.abs) atTop ⊓ 𝓟 {z | 0 < z.re}] fun z => expR (B * ↑Complex.abs z ^ c)\nhre : Tendsto (fun x => f ↑x) atTop (𝓝 0)\n... | [
750,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAt.const_sub | [] | [
367,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
8
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.integral_eq_zero_of_mul_right_eq_neg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.51091\nM : Type ?u.51094\nα : Type ?u.51097\nG : Type u_1\nE : Type u_2\nF : Type ?u.51106\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\nμ : Measure G\n... | [
145,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.J_mem | [
{
"state_after": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\n⊢ fromBlocks ((0 ⬝ 0 + (-1) ⬝ 1) ⬝ 0ᵀ + (0 ⬝ (-1) + (-1) ⬝ 0) ⬝ (-1)ᵀ)\n ((0 ⬝ 0 + (-1) ⬝ 1) ⬝ 1ᵀ + (0 ⬝ (-1) + (-1) ⬝ 0) ⬝ 0ᵀ) ((1 ⬝ 0 + 0 ⬝ 1) ⬝ 0ᵀ + (1 ⬝ (-1) + 0 ⬝ 0) ⬝ (-1)ᵀ)\n ((1 ⬝ 0 + ... | [
119,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_pred_of_lt | [] | [
474,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
473,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.degree_C_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\na : R\n⊢ degree (↑C a) = degree (↑C a * T 0)",
"tactic": "rw [T_zero, mul_one]"
}
] | [
557,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.