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/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.ιSummand_naturality_symm | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nS₁ S₂ : Split C\nΦ : S₁ ⟶ S₂\nΔ : SimplexCategoryᵒᵖ\nA : Splitting.IndexSet Δ\n⊢ Splitting.ιSummand S₁.s A ≫ Φ.F.app Δ = Hom.f Φ (len A.fst.unop) ≫ Splitting.ιSummand S₂.s A",
"tactic": "erw [... | [
464,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.trans | [] | [
156,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nδ : Type ?u.244028\ninst✝² : AddCommMonoid α\ninst✝¹ : TopologicalSpace α\nf✝ g : β → α\na✝ b : α\ns✝ : Finset β\ninst✝ : ContinuousAdd α\nf : γ → β → α\na : γ → α\ns : Finset γ\n⊢ (∀ (i : γ), i ∈ ∅ → HasSum (f i) (a i))... | [
327,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.range_eq_top | [
{
"state_after": "V : Type u\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : CompleteSpace V\nB : V →L[ℝ] V →L[ℝ] ℝ\ncoercive : IsCoercive B\nthis : CompleteSpace ↑↑(range (continuousLinearMapOfBilin B))\n⊢ range (continuousLinearMapOfBilin B) = ⊤",
"state_before": "V : Type u\ninst✝... | [
108,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/Order.lean | Continuous.le_induced | [] | [
415,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_inl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.119697\nδ : Type ?u.119700\nε : Type ?u.119703\nζ : Type ?u.119706\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nu : Set α\nhu : IsOpen u\n⊢ IsOpen (inl '' ... | [
902,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_comp_coe_Ioo_atTop | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf : α → β\nh : a < b\n⊢ Tendsto (fun x => f ↑x) atTop l ↔ Tendsto (f ∘ Subtype.val) atTop l",
"state_before": "α : ... | [
2534,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2532,
1
] |
Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.mem_iff_annIdealGenerator_dvd | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nA : Type u_2\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\ninst✝ : Algebra 𝕜 A\np : 𝕜[X]\na : A\n⊢ p ∈ annIdeal 𝕜 a ↔ annIdealGenerator 𝕜 a ∣ p",
"tactic": "rw [← Ideal.mem_span_singleton, span_singleton_annIdealGenerator]"
}
] | [
147,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/Convex/Segment.lean | mem_openSegment_translate | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.133397\nG : Type ?u.133400\nι : Type ?u.133403\nπ : ι → Type ?u.133408\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\na x b ... | [
270,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Finset.aestronglyMeasurable_prod' | [] | [
1420,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_le_mul_of_det_lt | [
{
"state_after": "case a\nE : Type u_1\nF : Type ?u.309008\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 : BorelSpace E\nμ : Measure E... | [
390,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | eqOn_dslope_slope | [] | [
59,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Order/Bounds/Basic.lean | MonotoneOn.image_upperBounds_subset_upperBounds_image | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\ns t : Set α\nHf : MonotoneOn f t\na✝ : α\nHst✝ Hst : s ⊆ t\na : α\nha : a ∈ upperBounds s ∩ t\n⊢ f a ∈ upperBounds (f '' s)",
"state_before": "α : Type u\nβ : Type v\nγ : T... | [
1175,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.piecewise_ite | [] | [
1465,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Data/Prod/TProd.lean | List.TProd.mk_elim | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nα : ι → Type v\ni✝ j : ι\nl : List ι\nf : (i : ι) → α i\ninst✝ : DecidableEq ι\nhnd : Nodup l\nh : ∀ (i : ι), i ∈ l\nv : TProd α l\ni : ι\nhi : i ∈ l\n⊢ TProd.elim (TProd.mk l (TProd.elim' h v)) hi = TProd.elim v hi",
"tactic": "simp [elim_mk]"
... | [
137,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_card | [] | [
942,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_one | [] | [
575,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_zero | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_mul_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf : R →+* S₁\ng : σ → S₁\n⊢ (eval₂ f g p * ↑f a * Finsupp.prod 0 fun n e => g n... | [
999,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.liftRel_of_mem | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\na : α\nb : β\nca : Computation α\ncb : Computation β\nma : a ∈ ca\nmb : b ∈ cb\nab : R a b\na' : α\nma' : a' ∈ ca\n⊢ ∃ b, b ∈ cb ∧ R a b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\na : α\nb : β\nca : Computa... | [
1132,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_inf | [
{
"state_after": "case h.mk.mk\nι : Sort ?u.70630\n𝕜 : Type ?u.70633\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\nG₁ G₂ : SimpleGraph V\nx✝ : Sym2 V\nx y : V\n⊢ Quot.mk Setoid.r (x, y) ∈ edgeSet (G₁ ⊓ G₂) ↔ Quot.mk Setoid.r (x, y) ∈ edgeSet G₁ ∩ edgeS... | [
531,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean | BoxIntegral.BoxAdditiveMap.map_split_add | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : Type u_2\nn : ℕ\nN : Type ?u.40368\ninst✝¹ : AddCommMonoid M\ninst✝ : AddCommMonoid N\nI₀ : WithTop (Box ι)\nI J : Box ι\ni✝ : ι\nf : ι →ᵇᵃ[I₀] M\nhI : ↑I ≤ I₀\ni : ι\nx : ℝ\n⊢ Option.elim' 0 (↑f) (splitLower I i x) + Option.elim' 0 (↑f) (split... | [
112,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.completeTheory.isSatisfiable | [] | [
501,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_iInf | [
{
"state_after": "ι : Sort u_1\ns : ι → ℝ≥0\n⊢ sInf (Set.range (toReal ∘ fun i => s i)) = sInf (Set.range fun i => ↑(s i))",
"state_before": "ι : Sort u_1\ns : ι → ℝ≥0\n⊢ ↑(⨅ (i : ι), s i) = ⨅ (i : ι), ↑(s i)",
"tactic": "rw [iInf, iInf, coe_sInf, ← Set.range_comp]"
},
{
"state_after": "no goals... | [
517,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.map_proj_nhds | [] | [
243,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.act'_symm_apply | [] | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.SignedMeasure.toMeasureOfZeroLE_toSignedMeasure | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.716310\nm : MeasurableSpace α\ns : SignedMeasure α\ni✝ j : Set α\nhs : restrict 0 Set.univ ≤ restrict s Set.univ\ni : Set α\n⊢ MeasurableSet i → ↑(Measure.toSignedMeasure (toMeasureOfZeroLE s Set.univ (_ : MeasurableSet Set.univ) hs)) i = ↑s i",
"state_bef... | [
1404,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_one | [] | [
2457,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2455,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Multiset.prod_ne_zero_of_prime | [] | [
170,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_idRel | [] | [
138,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Bool/Count.lean | List.Chain'.two_mul_count_bool_le_length_add_one | [
{
"state_after": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\n⊢ (if Even (length l) then length l else if (some b == head? l) = true then length l + 1 else length l - 1) ≤\n length l + 1",
"state_before": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\n⊢ 2 * count b l ≤... | [
138,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.unique_diff_preimage | [
{
"state_after": "𝕜 : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_1\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\ns : Set H\nhs : IsOpen s\n⊢ UniqueDiffOn 𝕜 (range ↑I ∩ ↑(ModelWithCorners.symm I) ⁻¹' s)",
"st... | [
328,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Submodule.finsupp_sum_mem | [] | [
1148,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
11
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.subtypeCongr.apply | [
{
"state_after": "no goals",
"state_before": "ε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\nep ep' : Perm { a // p a }\nen en' : Perm { a // ¬p a }\na : ε\n⊢ ↑(subtypeCongr ep en) a = if h : p a then ↑(↑ep { val := a, property := h }) else ↑(↑en { val := a, property := h })",
"tactic": "by_cases ... | [
561,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Std/Logic.lean | eq_comm | [] | [
104,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
104,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.OrdConnected.dual | [] | [
96,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Logic/Basic.lean | ite_eq_right_iff | [] | [
1155,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_of_one_le | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 1 ≤ x\n⊢ arcsin x = π / 2",
"tactic": "rw [← arcsin_projIcc, projIcc_of_right_le _ hx, Subtype.coe_mk, arcsin_one]"
}
] | [
125,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.card_disjSum | [] | [
54,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | IsOpen.measure_pos | [] | [
49,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/LocallyFinite.lean | Set.finite_Ioc | [] | [
657,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Std/Logic.lean | not_and_of_not_left | [] | [
231,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
231,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.of_respects_arrow_iso | [
{
"state_after": "case left\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.17335\ninst✝ : Category D\nP : MorphismProperty C\nhP : ∀ (f g : Arrow C), (f ≅ g) → P f.hom → P g.hom\n⊢ ∀ {X Y Z : C} (e : X ≅ Y) (f : Y ⟶ Z), P f → P (e.hom ≫ f)\n\ncase right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.17335\ninst✝ ... | [
184,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_add_one_eq | [] | [
821,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.max | [] | [
611,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.gc_ceil_coe | [] | [
274,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.dvd_iff_mod_eq_zero | [
{
"state_after": "m n : ZNum\n⊢ ↑n % ↑m = 0 ↔ ↑n % ↑m = ↑0",
"state_before": "m n : ZNum\n⊢ m ∣ n ↔ n % m = 0",
"tactic": "rw [← dvd_to_int, Int.dvd_iff_emod_eq_zero, ← to_int_inj, mod_to_int]"
},
{
"state_after": "no goals",
"state_before": "m n : ZNum\n⊢ ↑n % ↑m = 0 ↔ ↑n % ↑m = ↑0",
"t... | [
1778,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1777,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | IsOfFinOrder.mul | [] | [
637,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.of_duplicate_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\nx y : α\nh : x ∈+ y :: l\nhx : x ≠ y\n⊢ x ∈+ l",
"tactic": "simpa [duplicate_cons_iff, hx.symm] using h"
}
] | [
103,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.comp_id | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.extend_comp_eq' | [] | [
389,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.wOppSide | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/CharP/Basic.lean | iterate_frobenius | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁴ : CommSemiring R\nS : Type v\ninst✝³ : CommSemiring S\nf : R →* S\ng : R →+* S\np : ℕ\ninst✝² : Fact (Nat.Prime p)\ninst✝¹ : CharP R p\ninst✝ : CharP S p\nx y : R\nn : ℕ\n⊢ (↑(frobenius R p)^[n]) x = x ^ p ^ n",
"tactic": "induction n wi... | [
356,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.zero_le_degree_iff | [
{
"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.700995\n⊢ 0 ≤ degree p ↔ p ≠ 0",
"tactic": "rw [← not_lt, Nat.WithBot.lt_zero_iff, degree_eq_bot]"
}
] | [
1069,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_neg_of_pos_of_neg | [
{
"state_after": "a b : Int\nha : 0 < a\nhb : b < 0\nh : a * b < a * 0\n⊢ a * b < 0",
"state_before": "a b : Int\nha : 0 < a\nhb : b < 0\n⊢ a * b < 0",
"tactic": "have h : a * b < a * 0 := Int.mul_lt_mul_of_pos_left hb ha"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nha : 0 < ... | [
1198,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1196,
11
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.zero_compLinearMap | [
{
"state_after": "case H\nR : Type u_1\ninst✝¹⁴ : Semiring R\nM : Type u_3\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\nN : Type u_4\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : Module R N\nP : Type ?u.360842\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\nM' : Type ?u.360872\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : M... | [
566,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_lt_div_iff' | [
{
"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 / d ↔ a * d < c * b",
"tactic": "simpa only [div_eq_mul_inv] using mul_inv_lt_mul_inv_iff'"
}
] | [
972,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.PreEnvelGroupRel.symm | [] | [
652,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | le_iff_uniformContinuous_id | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.140996\nu v : UniformSpace α\n⊢ u ≤ v ↔ UniformContinuous id",
"tactic": "rw [uniformContinuous_iff, uniformSpace_comap_id, id]"
}
] | [
1306,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivWithinAt.cpow_const | [] | [
207,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_lt_ofReal_iff_of_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.807039\nβ : Type ?u.807042\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nhp : 0 ≤ p\n⊢ ENNReal.ofReal p < ENNReal.ofReal q ↔ p < q",
"tactic": "rw [ENNReal.ofReal, ENNReal.ofReal, coe_lt_coe, Real.toNNReal_lt_toNNReal_iff_of_nonneg hp]"
}
] | [
2110,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2108,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.mem_toSubring | [] | [
232,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.valid | [
{
"state_after": "no goals",
"state_before": "l m r : List Char\n⊢ l ++ (m ++ r) =\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len l },\n stopPos := { byteIdx := utf8Len l + utf8Len m } }.str.data ∧\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len ... | [
791,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
790,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.iInf_biSup_of_monotone | [] | [
1489,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1486,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | exists_dist_le_le | [
{
"state_after": "case inl\n𝕜 : Type ?u.208107\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx y z : E\nδ : ℝ\nhδ : 0 ≤ δ\nhε : 0 ≤ 0\nh : dist x z ≤ 0 + δ\n⊢ ∃ y, dist x y ≤ δ ∧ dist y z ≤ 0\n\ncase inr\n𝕜 : Type ?u.208107\nE : ... | [
175,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Topology/Order/Basic.lean | StrictMono.embedding_of_ordConnected | [] | [
1073,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupNorm.le_def | [] | [
931,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | finrank_le_one_iff | [
{
"state_after": "case mp\nK : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\n⊢ finrank K V ≤ 1 → ∃ v, ∀ (w : V), ∃ c, c • v = w\n\ncase mpr\nK : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\n... | [
1305,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_piEquivPiSubtypeProd | [] | [
930,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_eq_zero_of_left | [] | [
238,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.reduct_withConstants | [
{
"state_after": "case h\nL : Language\nM : Type w\nN : Type ?u.671067\nP : Type ?u.671070\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\nA s : Set M\nh : A ⊆ ↑S\nx✝ : M\n⊢ x✝ ∈ ↑(LHom.substructureReduct (lhomWithConstants L ↑A)) (withConstants S h) ↔ x✝ ∈ S",
... | [
767,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.inner_left_fintype | [] | [
831,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.mkAlgHom_rel | [
{
"state_after": "no goals",
"state_before": "R : Type u₁\ninst✝⁴ : Semiring R\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nr : R → R → Prop\nT : Type u₄\ninst✝ : Semiring T\ns : A → A → Prop\nx y : A\nw : s x y\n⊢ ↑(mkAlgHom S s) x = ↑(mkAlgHom S s) y",
... | [
604,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Order/UpperLower/Hom.lean | UpperSet.icisSupHom_apply | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/List/Lattice.lean | List.inter_cons_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁✝ l₂ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₁ : List α\nh : ¬a ∈ l₂\n⊢ (a :: l₁) ∩ l₂ = l₁ ∩ l₂",
"tactic": "simp only [instInterList, List.inter, filter_cons_of_neg, h]"
}
] | [
152,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.range_evalᵢ | [
{
"state_after": "σ K : Type u\ninst✝² : Fintype K\ninst✝¹ : Field K\ninst✝ : Finite σ\n⊢ Submodule.map (evalₗ K σ) (restrictDegree σ K (Fintype.card K - 1)) = ⊤",
"state_before": "σ K : Type u\ninst✝² : Fintype K\ninst✝¹ : Field K\ninst✝ : Finite σ\n⊢ range (evalᵢ σ K) = ⊤",
"tactic": "rw [evalᵢ, Linea... | [
244,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.map_zero | [] | [
491,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
11
] |
Mathlib/Data/Real/Basic.lean | Real.sSup_univ | [] | [
826,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_eqOn_closedBall_of_isMaxOn | [
{
"state_after": "E : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nz : E\nr : ℝ\nhd : DiffContOnCl ℂ f (ball z r)\nhz : IsMaxOn (norm ∘ f) (ball z r) z\nw : E\nhw : w ∈ closedBall z r\n⊢ (norm ∘ f) w = Function.co... | [
199,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | LinearIsometryEquiv.reflections_generate_dim | [] | [
1217,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1214,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.traverse_mul' | [] | [
258,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coe_vadd | [] | [
415,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_one_add | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.138627\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group G\na : G\ni : ℤ\n⊢ a ^ (1 + i) = a * a ^ i",
"tactic": "rw [zpow_add, zpow_one]"
}
] | [
250,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.vecMul_neg | [
{
"state_after": "case h\nl : Type ?u.908244\nm : Type u_1\nn : Type u_2\no : Type ?u.908253\nm' : o → Type ?u.908258\nn' : o → Type ?u.908263\nR : Type ?u.908266\nS : Type ?u.908269\nα : Type v\nβ : Type w\nγ : Type ?u.908276\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : Fintype m\nv : m → α\nA : Matrix m n α\nx✝... | [
1903,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1901,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.cancel_right | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.136049\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.136061\ninst✝⁷ : Preorder α\ninst✝⁶ : Preorder β\ninst✝⁵ : Preorder γ\ninst✝⁴ : Preorder δ\ninst✝³ : MulZeroOneClass α\ninst✝² : MulZeroOneClass β\ninst✝¹ : MulZeroOneClass γ\ninst✝ : MulZ... | [
717,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.isIso_of_epi_of_isSplitMono | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : IsSplitMono f\ninst✝ : Epi f\n⊢ f ≫ retraction f = 𝟙 X",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nX Y : C\nf : X ⟶ Y\ninst✝... | [
126,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_quot_lift | [] | [
963,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_eq_fderiv | [
{
"state_after": "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.352325\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.352420\... | [
659,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_apply_eq | [] | [
366,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullbackIsoProdSubtype_inv_snd | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nX Y Z : TopCat\nf : X ⟶ Z\ng : Y ⟶ Z\n⊢ (pullbackIsoProdSubtype f g).inv ≫ pullback.snd = pullbackSnd f g",
"tactic": "simp [pullbackCone, pullbackIsoProdSubtype]"
}
] | [
116,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_lt | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.750411\ninst✝ : DecidableEq α\nl : List α\nx : α\nxs✝ : List α\nh✝ : Nodup xs✝\nn : ℕ\nhn✝ : n + 1 < length xs✝\nxs : List α\nh : Nodup xs\nhn : Nat.zero + 1 < length xs\n⊢ ↑(formPerm xs) (nthLe xs Nat.zero (_ : Nat.zero < length xs)) = nthLe xs (Nat.zero +... | [
226,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.symm_apply_apply | [] | [
786,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gaugeSeminorm_ball_one | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.250152\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\na : ℝ\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\nhs₀ : Balanced 𝕜 s\nhs₁ : Convex ℝ s\nhs₂ : Absorbent ℝ s\ninst✝¹ : TopologicalSpace E\ninst✝ : Continuou... | [
412,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableOn.continuousOn | [] | [
743,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.mul_den_dvd | [
{
"state_after": "q₁ q₂ : ℚ\n⊢ (mk' (q₁.num * q₂.num / ↑(Nat.gcd (Int.natAbs (q₁.num * q₂.num)) (q₁.den * q₂.den)))\n (q₁.den * q₂.den / Nat.gcd (Int.natAbs (q₁.num * q₂.num)) (q₁.den * q₂.den))).den ∣\n q₁.den * q₂.den",
"state_before": "q₁ q₂ : ℚ\n⊢ (q₁ * q₂).den ∣ q₁.den * q₂.den",
"tactic"... | [
86,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.of_fintype_basis | [
{
"state_after": "case intro\nK : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\nι : Type w\ninst✝ : _root_.Finite ι\nh : Basis ι K V\nval✝ : Fintype ι\n⊢ FiniteDimensional K V",
"state_before": "K : Ty... | [
148,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.compl_univ | [] | [
188,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_le_subfield | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nK : Subfield E\nHF : Set.range ↑(algebraMap F E) ⊆ ↑K\nHS : S ⊆ ↑K\n⊢ Set.range ↑(algebraMap F E) ∪ S ⊆ ↑K",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst... | [
360,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteEdges_coe_eq | [
{
"state_after": "case Adj.h.mk.h.mk.a\nι : Sort ?u.244319\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns✝ : Set (Sym2 V)\ns : Set (Sym2 ↑G'.verts)\nv : V\nhv : v ∈ G'.verts\nw : V\nhw : w ∈ G'.verts\n⊢ SimpleGraph.Adj (SimpleGraph.deleteEdges (Subgraph.coe G') s) { val := v, property := hv }\n ... | [
1078,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_bot_right | [] | [
112,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.