path stringlengths 12 84 | imports listlengths 0 4.45k | premises listlengths 0 625 |
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Mathlib/Data/Rbtree/Find.lean | [
"Mathlib/Mathport/Rename.lean",
".lake/packages/lean4/src/lean/Init.lean"
] | [] |
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | [
"Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
"Mathlib/Combinatorics/SimpleGraph/Basic.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Data/Set/Finite.lean",
"Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean"
] | [
{
"full_name": "SimpleGraph.IsSRGWith",
"code": "structure IsSRGWith (n k β ΞΌ : β) : Prop where\n card : Fintype.card V = n\n regular : G.IsRegularOfDegree k\n of_adj : β v w : V, G.Adj v w β Fintype.card (G.commonNeighbors v w) = β\n of_not_adj : Pairwise fun v w => Β¬G.Adj v w β Fintype.card (G.commonN... |
Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Algebra/DirectLimit.lean"
] | [
{
"full_name": "TensorProduct.fromDirectLimit",
"code": "noncomputable def fromDirectLimit :\n DirectLimit (G Β· β[R] M) (f β· M) ββ[R] DirectLimit G f β[R] M :=\n DirectLimit.lift _ _ _ _ (fun _ β¦ (of _ _ _ _ _).rTensor M)\n fun _ _ _ x β¦ by refine x.induction_on ?_ ?_ ?_ <;> aesop",
"start": [
... |
Mathlib/Analysis/Convex/Quasiconvex.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/Convex/Function.lean"
] | [
{
"full_name": "QuasiconvexOn",
"code": "def QuasiconvexOn : Prop :=\n β r, Convex π ({ x β s | f x β€ r })",
"start": [
48,
1
],
"end": [
51,
38
],
"kind": "commanddeclaration"
},
{
"full_name": "QuasiconcaveOn",
"code": "def QuasiconcaveOn : Prop :=... |
Mathlib/Algebra/AddConstMap/Basic.lean | [
"Mathlib/Algebra/Module/Defs.lean",
"Mathlib/Algebra/Order/Group/Instances.lean",
"Mathlib/Logic/Function/Iterate.lean",
"Mathlib/Algebra/GroupPower/IterateHom.lean",
"Mathlib/GroupTheory/GroupAction/Pi.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Algebra/Order/Archimedean.lean"
] | [
{
"full_name": "AddConstMap",
"code": "structure AddConstMap (G H : Type*) [Add G] [Add H] (a : G) (b : H) where\n \n protected toFun : G β H\n \n map_add_const' (x : G) : toFun (x + a) = toFun x + b",
"start": [
33,
1
],
"end": [
41,
55
],
"kind": "commanddec... |
Mathlib/Probability/BorelCantelli.lean | [
"Mathlib/Probability/ConditionalExpectation.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Probability/Martingale/BorelCantelli.lean",
"Mathlib/Probability/Independence/Basic.lean"
] | [
{
"full_name": "ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt",
"code": "theorem iIndepFun.indep_comap_natural_of_lt (hf : β i, StronglyMeasurable (f i))\n (hfi : iIndepFun (fun _ => mΞ²) f ΞΌ) (hij : i < j) :\n Indep (MeasurableSpace.comap (f j) mΞ²) (Filtration.natural f hf i) ΞΌ",
"start": ... |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Combinatorics/SetFamily/Shadow.lean"
] | [
{
"full_name": "sup_sdiff_injOn",
"code": "theorem sup_sdiff_injOn [GeneralizedBooleanAlgebra Ξ±] (u v : Ξ±) :\n { x | Disjoint u x β§ v β€ x }.InjOn fun x => (x β u) \\ v",
"start": [
56,
1
],
"end": [
64,
89
],
"kind": "commanddeclaration"
},
{
"full_name... |
Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean | [
"Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean",
".lake/packages/lean4/src/lean/Init.lean"
] | [
{
"full_name": "AffineSubspace.pointwiseAddAction",
"code": "protected def pointwiseAddAction : AddAction V (AffineSubspace k P) where\n vadd x S := S.map (AffineEquiv.constVAdd k P x)\n zero_vadd p := ((congr_arg fun f => p.map f) <| AffineMap.ext <| zero_vadd _).trans p.map_id\n add_vadd _ _ p :=\n ... |
Mathlib/Lean/CoreM.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Tactic/ToExpr.lean"
] | [
{
"full_name": "CoreM.withImportModules",
"code": "def CoreM.withImportModules (modules : Array Name) (run : CoreM Ξ±)\n (searchPath : Option SearchPath := none) (options : Options := {})\n (trustLevel : UInt32 := 0) (fileName := \"\") :\n IO Ξ± := unsafe do\n if let some sp := searchPath then searc... |
Mathlib/Algebra/Algebra/Subalgebra/Rank.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/LinearAlgebra/Dimension/Free.lean",
"Mathlib/LinearAlgebra/FreeModule/StrongRankCondition.lean",
"Mathlib/LinearAlgebra/Dimension/Finite.lean"
] | [
{
"full_name": "Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free",
"code": "theorem rank_sup_eq_rank_left_mul_rank_of_free :\n Module.rank R β₯(A β B) = Module.rank R A * Module.rank A (Algebra.adjoin A (B : Set S))",
"start": [
30,
1
],
"end": [
41,
43
],
"kin... |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | [
"Mathlib/Analysis/Convex/Hull.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/LinearAlgebra/AffineSpace/Independent.lean"
] | [
{
"full_name": "Geometry.SimplicialComplex",
"code": "@[ext]\nstructure SimplicialComplex where\n \n faces : Set (Finset E)\n \n not_empty_mem : β
β faces\n \n indep : β {s}, s β faces β AffineIndependent π ((β) : s β E)\n \n down_closed : β {s t}, s β faces β t β s β t β β
β t β faces\n inter_sub... |
Mathlib/Analysis/Calculus/Gradient/Basic.lean | [
"Mathlib/Analysis/Calculus/FDeriv/Basic.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/InnerProductSpace/Dual.lean",
"Mathlib/Analysis/Calculus/Deriv/Basic.lean"
] | [
{
"full_name": "HasGradientAtFilter",
"code": "def HasGradientAtFilter (f : F β π) (f' x : F) (L : Filter F) :=\n HasFDerivAtFilter f (toDual π F f') x L",
"start": [
48,
1
],
"end": [
51,
42
],
"kind": "commanddeclaration"
},
{
"full_name": "HasGradien... |
Mathlib/LinearAlgebra/TensorAlgebra/Grading.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/RingTheory/GradedAlgebra/Basic.lean",
"Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean"
] | [
{
"full_name": "TensorAlgebra.GradedAlgebra.ΞΉ",
"code": "nonrec def GradedAlgebra.ΞΉ : M ββ[R] β¨ i : β, β₯(LinearMap.range (ΞΉ R : M ββ[_] _) ^ i) :=\n DirectSum.lof R β (fun i => β₯(LinearMap.range (ΞΉ R : M ββ[_] _) ^ i)) 1 ββ\n (ΞΉ R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range... |
Mathlib/Data/QPF/Multivariate/Constructions/Const.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Control/Functor/Multivariate.lean",
"Mathlib/Data/QPF/Multivariate/Basic.lean"
] | [
{
"full_name": "MvQPF.Const",
"code": "@[nolint unusedArguments]\ndef Const (A : Type*) (_v : TypeVec.{u} n) : Type _ := A",
"start": [
30,
1
],
"end": [
32,
57
],
"kind": "commanddeclaration"
},
{
"full_name": "MvQPF.Const.inhabited",
"code": "instanc... |
Mathlib/Combinatorics/Configuration.lean | [
"Mathlib/Combinatorics/Hall/Basic.lean",
"Mathlib/Data/Fintype/BigOperators.lean",
"Mathlib/SetTheory/Cardinal/Finite.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Algebra/Order/BigOperators/Group/Finset.lean"
] | [
{
"full_name": "Configuration.Dual",
"code": "def Dual :=\n P",
"start": [
44,
1
],
"end": [
46,
4
],
"kind": "commanddeclaration"
},
{
"full_name": "Configuration.Nondegenerate",
"code": "class Nondegenerate : Prop where\n exists_point : β l : L, β ... |
Mathlib/FieldTheory/Laurent.lean | [
"Mathlib/Algebra/Polynomial/Taylor.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/FieldTheory/RatFunc/AsPolynomial.lean"
] | [
{
"full_name": "RatFunc.taylor_mem_nonZeroDivisors",
"code": "theorem taylor_mem_nonZeroDivisors (hp : p β R[X]β°) : taylor r p β R[X]β°",
"start": [
39,
1
],
"end": [
45,
60
],
"kind": "commanddeclaration"
},
{
"full_name": "RatFunc.laurentAux",
"code":... |
Mathlib/LinearAlgebra/Matrix/Dual.lean | [
"Mathlib/LinearAlgebra/Dual.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/LinearAlgebra/Matrix/ToLin.lean"
] | [
{
"full_name": "LinearMap.toMatrix_transpose",
"code": "@[simp]\ntheorem LinearMap.toMatrix_transpose (u : Vβ ββ[K] Vβ) :\n LinearMap.toMatrix Bβ.dualBasis Bβ.dualBasis (Module.Dual.transpose (R := K) u) =\n (LinearMap.toMatrix Bβ Bβ u)α΅",
"start": [
31,
1
],
"end": [
3... |
Mathlib/Geometry/Euclidean/Sphere/Ptolemy.lean | [
"Mathlib/Geometry/Euclidean/Sphere/Power.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Geometry/Euclidean/Triangle.lean"
] | [
{
"full_name": "EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical",
"code": "theorem mul_dist_add_mul_dist_eq_mul_dist_of_cospherical {a b c d p : P}\n (h : Cospherical ({a, b, c, d} : Set P)) (hapc : β a p c = Ο) (hbpd : β b p d = Ο) :\n dist a b * dist c d + dist b c * dist d a = di... |
Mathlib/Topology/Order/Hom/Esakia.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Order/Hom/Bounded.lean",
"Mathlib/Topology/Order/Hom/Basic.lean"
] | [
{
"full_name": "PseudoEpimorphism",
"code": "structure PseudoEpimorphism (Ξ± Ξ² : Type*) [Preorder Ξ±] [Preorder Ξ²] extends Ξ± βo Ξ² where\n exists_map_eq_of_map_le' β¦a : Ξ±β¦ β¦b : Ξ²β¦ : toFun a β€ b β β c, a β€ c β§ toFun c = b",
"start": [
40,
1
],
"end": [
42,
84
],
"kin... |
Mathlib/Analysis/Convex/EGauge.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/Seminorm.lean"
] | [
{
"full_name": "egauge",
"code": "noncomputable def egauge (π : Type*) [NNNorm π] {E : Type*} [SMul π E] (s : Set E) (x : E) : ββ₯0β :=\n β¨
(c : π) (_ : x β c β’ s), βcββ",
"start": [
32,
1
],
"end": [
43,
34
],
"kind": "commanddeclaration"
},
{
"full_n... |
Mathlib/CategoryTheory/Localization/FiniteProducts.lean | [
"Mathlib/CategoryTheory/Localization/HasLocalization.lean",
"Mathlib/CategoryTheory/Localization/Adjunction.lean",
"Mathlib/CategoryTheory/MorphismProperty/Limits.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/CategoryTheory/Limits/Preserves/Finite.lean",
"Mathlib/CategoryTheory/Limits/ConeCat... | [
{
"full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.inverts",
"code": "lemma inverts :\n (W.functorCategory (Discrete J)).IsInvertedBy (lim β L) :=\n fun _ _ f hf => Localization.inverts L W _ (hW.lim_map f hf)",
"start": [
38,
1
],
"end": [
40,
63
]... |
Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean | [
"Mathlib/MeasureTheory/Function/ContinuousMapDense.lean",
"Mathlib/MeasureTheory/Integral/SetIntegral.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/Fourier/FourierTransform.lean",
"Mathlib/Analysis/InnerProductSpace/Dual.lean",
"Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean",... | [
{
"full_name": "fourierIntegral_half_period_translate",
"code": "theorem fourierIntegral_half_period_translate {w : V} (hw : w β 0) :\n (β« v : V, π (-βͺv, wβ«) β’ f (v + i w)) = -β« v : V, π (-βͺv, wβ«) β’ f v",
"start": [
67,
1
],
"end": [
92,
37
],
"kind": "comman... |
Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean | [
"Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/NormedSpace/FiniteDimension.lean"
] | [
{
"full_name": "ApproximatesLinearOn.exists_homeomorph_extension",
"code": "theorem exists_homeomorph_extension {E : Type*} [NormedAddCommGroup E] [NormedSpace β E]\n {F : Type*} [NormedAddCommGroup F] [NormedSpace β F] [FiniteDimensional β F] {s : Set E}\n {f : E β F} {f' : E βL[β] F} {c : ββ₯0} (hf :... |
Mathlib/Analysis/Convex/Radon.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/Convex/Combination.lean",
"Mathlib/Tactic/Linarith.lean"
] | [
{
"full_name": "radon_partition",
"code": "theorem radon_partition (h : Β¬ AffineIndependent π f) :\n β I, (convexHull π (f '' I) β© convexHull π (f '' IαΆ)).Nonempty",
"start": [
24,
1
],
"end": [
50,
60
],
"kind": "commanddeclaration"
}
] |
Mathlib/RepresentationTheory/Character.lean | [
"Mathlib/LinearAlgebra/Trace.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/RepresentationTheory/Invariants.lean",
"Mathlib/RepresentationTheory/FdRep.lean"
] | [
{
"full_name": "FdRep.character",
"code": "def character (V : FdRep k G) (g : G) :=\n LinearMap.trace k V (V.Ο g)",
"start": [
48,
1
],
"end": [
51,
30
],
"kind": "commanddeclaration"
},
{
"full_name": "FdRep.char_mul_comm",
"code": "theorem char_mul_... |
Mathlib/Algebra/Homology/HomotopyCategory/SingleFunctors.lean | [
"Mathlib/CategoryTheory/Shift/SingleFunctors.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Algebra/Homology/HomotopyCategory/Shift.lean"
] | [
{
"full_name": "CochainComplex.singleFunctors",
"code": "noncomputable def singleFunctors : SingleFunctors C (CochainComplex C β€) β€ where\n functor n := single _ _ n\n shiftIso n a a' ha' := NatIso.ofComponents\n (fun X => Hom.isoOfComponents\n (fun i => eqToIso (by\n obtain rfl : a' = a + ... |
Mathlib/Algebra/Lie/CartanMatrix.lean | [
"Mathlib/Data/Matrix/Notation.lean",
"Mathlib/Algebra/Lie/Quotient.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Algebra/Lie/Free.lean"
] | [
{
"full_name": "CartanMatrix.Generators",
"code": "inductive Generators\n | H : B β Generators\n | E : B β Generators\n | F : B β Generators",
"start": [
96,
1
],
"end": [
101,
23
],
"kind": "commanddeclaration"
},
{
"full_name": "CartanMatrix.Relations... |
Mathlib/SetTheory/ZFC/Ordinal.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/SetTheory/ZFC/Basic.lean"
] | [
{
"full_name": "ZFSet.IsTransitive",
"code": "def IsTransitive (x : ZFSet) : Prop :=\n β y β x, y β x",
"start": [
39,
1
],
"end": [
41,
17
],
"kind": "commanddeclaration"
},
{
"full_name": "ZFSet.empty_isTransitive",
"code": "@[simp]\ntheorem empty_i... |
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/InnerProductSpace/Dual.lean"
] | [
{
"full_name": "IsCoercive.bounded_below",
"code": "theorem bounded_below (coercive : IsCoercive B) : β C, 0 < C β§ β v, C * βvβ β€ βBβ― vβ",
"start": [
51,
1
],
"end": [
62,
16
],
"kind": "commanddeclaration"
},
{
"full_name": "IsCoercive.antilipschitz",
... |
Mathlib/Data/Buffer/Basic.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Init/Align.lean"
] | [] |
Mathlib/NumberTheory/SiegelsLemma.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Tactic/Rify.lean",
"Mathlib/Analysis/Matrix.lean",
"Mathlib/Data/Pi/Interval.lean"
] | [
{
"full_name": "Int.Matrix.image_T_subset_S",
"code": "private lemma image_T_subset_S (v) (hv : v β T) : A *α΅₯ v β S := by\n rw [mem_Icc] at hv β’\n have mulVec_def : A.mulVec v =\n fun i β¦ Finset.sum univ fun j : Fin n β¦ A i j * v j := rfl\n rw [mulVec_def]\n refine β¨fun i β¦ ?_, fun i β¦ ?_β©\n all_g... |
Mathlib/Data/ZMod/Coprime.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/RingTheory/PrincipalIdealDomain.lean",
"Mathlib/Data/ZMod/Basic.lean",
"Mathlib/RingTheory/Int/Basic.lean"
] | [
{
"full_name": "ZMod.eq_zero_iff_gcd_ne_one",
"code": "theorem eq_zero_iff_gcd_ne_one {a : β€} {p : β} [pp : Fact p.Prime] :\n (a : ZMod p) = 0 β a.gcd p β 1",
"start": [
22,
1
],
"end": [
28,
34
],
"kind": "commanddeclaration"
},
{
"full_name": "ZMod.ne... |
Mathlib/Data/Finset/Functor.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Data/Finset/NAry.lean",
"Mathlib/Data/Finset/Lattice.lean",
"Mathlib/Data/Multiset/Functor.lean"
] | [
{
"full_name": "Finset.functor",
"code": "protected instance functor : Functor Finset where map f s := s.image f",
"start": [
37,
1
],
"end": [
39,
71
],
"kind": "commanddeclaration"
},
{
"full_name": "Finset.lawfulFunctor",
"code": "instance lawfulFun... |
Mathlib/Data/UInt.lean | [
"Mathlib/Data/ZMod/Defs.lean",
".lake/packages/lean4/src/lean/Init.lean"
] | [
{
"full_name": "neZero",
"code": "instance neZero : NeZero size := β¨by decideβ©",
"start": [
31,
7
],
"end": [
31,
51
],
"kind": "commanddeclaration"
},
{
"full_name": "neg_def",
"code": "lemma neg_def (a : $typeName) : -a = β¨-a.valβ© := rfl",
"start... |
Mathlib/Order/Category/OmegaCompletePartialOrder.lean | [
"Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
"Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean",
"Mathlib/Order/OmegaCompletePartialOrder.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean",
"Mathlib/CategoryTheory... | [
{
"full_name": "ΟCPO",
"code": "def ΟCPO : Type (u + 1) :=\n Bundled OmegaCompletePartialOrder",
"start": [
35,
1
],
"end": [
37,
36
],
"kind": "commanddeclaration"
},
{
"full_name": "ΟCPO.of",
"code": "def of (Ξ± : Type*) [OmegaCompletePartialOrder Ξ±]... |
Mathlib/Analysis/Calculus/Rademacher.lean | [
"Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean",
"Mathlib/MeasureTheory/Measure/Haar/Disintegration.lean",
"Mathlib/Analysis/BoundedVariation.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/NormedSpace/FiniteDimension.lean",
"Mathlib/MeasureTheory/Group/Integral.lean",
"Mathlib/... | [
{
"full_name": "LipschitzWith.ae_lineDifferentiableAt",
"code": "theorem ae_lineDifferentiableAt (hf : LipschitzWith C f) (v : E) :\n βα΅ p βΞΌ, LineDifferentiableAt β f p v",
"start": [
63,
1
],
"end": [
77,
77
],
"kind": "commanddeclaration"
},
{
"full_... |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | [
"Mathlib/Analysis/Complex/Circle.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Analysis/NormedSpace/BallAction.lean"
] | [
{
"full_name": "Complex.UnitDisc",
"code": "def UnitDisc : Type :=\n ball (0 : β) 1 deriving TopologicalSpace",
"start": [
27,
1
],
"end": [
29,
43
],
"kind": "commanddeclaration"
},
{
"full_name": "Complex.UnitDisc.instCommSemigroup",
"code": "instan... |
Mathlib/Algebra/Order/Group/Bounds.lean | [
"Mathlib/Algebra/Order/Group/Defs.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Order/Bounds/Basic.lean"
] | [
{
"full_name": "IsGLB.exists_between_self_add",
"code": "theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hΞ΅ : 0 < Ξ΅) : β b β s, a β€ b β§ b < a + Ξ΅",
"start": [
19,
1
],
"end": [
20,
47
],
"kind": "commanddeclaration"
},
{
"full_name": "IsGLB.exists_b... |
Mathlib/Lean/Expr.lean | [
"Mathlib/Lean/Expr/Basic.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Lean/Expr/ReplaceRec.lean"
] | [] |
Mathlib/CategoryTheory/Limits/EpiMono.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean"
] | [
{
"full_name": "CategoryTheory.mono_iff_fst_eq_snd",
"code": "lemma mono_iff_fst_eq_snd : Mono f β c.fst = c.snd := by\n constructor\n Β· intro hf\n simpa only [β cancel_mono f] using c.condition\n Β· intro hf\n constructor\n intro Z g g' h\n obtain β¨Ο, rfl, rflβ© := PullbackCone.IsLimit.lift' h... |
Mathlib/Data/Vector/Mem.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Data/Vector/Basic.lean"
] | [
{
"full_name": "Vector.get_mem",
"code": "@[simp]\ntheorem get_mem (i : Fin n) (v : Vector Ξ± n) : v.get i β v.toList",
"start": [
25,
1
],
"end": [
28,
27
],
"kind": "commanddeclaration"
},
{
"full_name": "Vector.mem_iff_get",
"code": "theorem mem_iff_... |
Mathlib/CategoryTheory/Functor/Derived/RightDerived.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/CategoryTheory/Localization/Predicate.lean",
"Mathlib/CategoryTheory/Functor/KanExtension/Basic.lean"
] | [
{
"full_name": "CategoryTheory.Functor.IsRightDerivedFunctor",
"code": "class IsRightDerivedFunctor [L.IsLocalization W] : Prop where\n isLeftKanExtension' : RF.IsLeftKanExtension Ξ±",
"start": [
47,
1
],
"end": [
52,
48
],
"kind": "commanddeclaration"
},
{
... |
Mathlib/NumberTheory/Modular.lean | [
"Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean",
"Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean",
"Mathlib/Topology/Algebra/Module/FiniteDimension.lean",
"Mathlib/LinearAlgebra/GeneralLinearGroup.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Topology/Instances/Matrix.lean"
] | [
{
"full_name": "ModularGroup.bottom_row_coprime",
"code": "theorem bottom_row_coprime {R : Type*} [CommRing R] (g : SL(2, R)) :\n IsCoprime ((βg : Matrix (Fin 2) (Fin 2) R) 1 0) ((βg : Matrix (Fin 2) (Fin 2) R) 1 1)",
"start": [
84,
1
],
"end": [
89,
18
],
"kin... |
Mathlib/Topology/ContinuousFunction/Sigma.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Topology/CompactOpen.lean"
] | [
{
"full_name": "ContinuousMap.embedding_sigmaMk_comp",
"code": "theorem embedding_sigmaMk_comp [Nonempty X] :\n Embedding (fun g : Ξ£ i, C(X, Y i) β¦ (sigmaMk g.1).comp g.2) where",
"start": [
44,
1
],
"end": [
54,
21
],
"kind": "commanddeclaration"
},
{
... |
Mathlib/Data/Finset/NatDivisors.lean | [
"Mathlib/Data/Nat/Order/Lemmas.lean",
"Mathlib/Data/Finset/Pointwise.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/NumberTheory/Divisors.lean"
] | [
{
"full_name": "Nat.divisors_mul",
"code": "lemma Nat.divisors_mul (m n : β) : divisors (m * n) = divisors m * divisors n := by\n ext k\n simp_rw [mem_mul, mem_divisors, dvd_mul, mul_ne_zero_iff, β exists_and_left, β exists_and_right]\n simp only [and_assoc, and_comm, and_left_comm]",
"start": [
... |
Mathlib/GroupTheory/GroupAction/Sum.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/Algebra/Group/Action/Defs.lean"
] | [
{
"full_name": "Sum.smul_def",
"code": "@[to_additive]\ntheorem smul_def : a β’ x = x.map (a β’ Β·) (a β’ Β·)",
"start": [
37,
1
],
"end": [
39,
6
],
"kind": "commanddeclaration"
},
{
"full_name": "Sum.smul_inl",
"code": "@[to_additive (attr := simp)]\ntheo... |
Mathlib/Init/Data/Int/Lemmas.lean | [
"Mathlib/Mathport/Rename.lean",
".lake/packages/lean4/src/lean/Init.lean"
] | [] |
Mathlib/NumberTheory/PrimesCongruentOne.lean | [
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean"
] | [
{
"full_name": "Nat.exists_prime_gt_modEq_one",
"code": "theorem exists_prime_gt_modEq_one {k : β} (n : β) (hk0 : k β 0) :\n β p : β, Nat.Prime p β§ n < p β§ p β‘ 1 [MOD k]",
"start": [
24,
1
],
"end": [
57,
54
],
"kind": "commanddeclaration"
},
{
"full_na... |
Mathlib/LinearAlgebra/TensorProduct/Matrix.lean | [
"Mathlib/LinearAlgebra/TensorProduct/Basis.lean",
".lake/packages/lean4/src/lean/Init.lean",
"Mathlib/LinearAlgebra/Matrix/ToLin.lean",
"Mathlib/Data/Matrix/Kronecker.lean"
] | [
{
"full_name": "TensorProduct.toMatrix_map",
"code": "theorem TensorProduct.toMatrix_map (f : M ββ[R] M') (g : N ββ[R] N') :\n toMatrix (bM.tensorProduct bN) (bM'.tensorProduct bN') (TensorProduct.map f g) =\n toMatrix bM bM' f ββ toMatrix bN bN' g",
"start": [
37,
1
],
"end"... |
.lake/packages/lean4/src/lean/Lean/Compiler/IR/LLVMBindings.lean | [
".lake/packages/lean4/src/lean/Init/System/IO.lean"
] | [
{
"full_name": "LLVM.CodegenFileType",
"code": "structure CodegenFileType where\n private mk :: val : UInt64",
"start": [
20,
1
],
"end": [
21,
29
],
"kind": "commanddeclaration"
},
{
"full_name": "LLVM.CodegenFileType.AssemblyFile",
"code": "def Code... |
.lake/packages/lean4/src/lean/lake/Lake.lean | [
".lake/packages/lean4/src/lean/lake/Lake/Config.lean",
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/lean4/src/lean/lake/Lake/Toml.lean",
".lake/packages/lean4/src/lean/lake/Lake/DSL.lean",
".lake/packages/lean4/src/lean/lake/Lake/Version.lean",
".lake/packages/lean4/src/lean/lake/Lake/Build.... | [] |
.lake/packages/lean4/src/lean/lake/Lake/CLI.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/lean4/src/lean/lake/Lake/CLI/Main.lean"
] | [] |
Mathlib.lean | [
"Mathlib/Data/Finset/Union.lean",
"Mathlib/LinearAlgebra/TensorProduct/Matrix.lean",
"Mathlib/NumberTheory/PrimesCongruentOne.lean",
"Mathlib/Init/Data/Int/Lemmas.lean",
"Mathlib/Topology/Homotopy/Equiv.lean",
"Mathlib/CategoryTheory/Functor/Functorial.lean",
"Mathlib/GroupTheory/GroupAction/Sum.lean",
... | [] |
.lake/packages/proofwidgets/ProofWidgets/Demos/Conv.lean | [
".lake/packages/lean4/src/lean/Lean/Meta/ExprLens.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean",
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.l... | [
{
"full_name": "NewCursorPos",
"code": "structure NewCursorPos where\n newCursorPos? : Option Lsp.Position\n uri? : Option String\n deriving ToJson, FromJson",
"start": [
17,
1
],
"end": [
20,
28
],
"kind": "commanddeclaration"
},
{
"full_name": "SolveR... |
.lake/packages/proofwidgets/ProofWidgets/Demos/SelectInsertConv.lean | [
".lake/packages/lean4/src/lean/Lean/Meta/ExprLens.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean",
".lake/packages/batteries/Batteries/Lean/Position.lean",
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean",
".lake... | [
{
"full_name": "SolveReturn",
"code": "private structure SolveReturn where\n expr : Expr\n val? : Option String\n listRest : List Nat",
"start": [
23,
1
],
"end": [
26,
22
],
"kind": "commanddeclaration"
},
{
"full_name": "solveLevel",
"code": "priv... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Plot.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/Recharts.lean"
] | [
{
"full_name": "fn",
"code": "def fn (t : Float) (x : Float): Float :=\n 50 * (x - 0.25) * (x - 0.5) * (x - 0.7) + 0.1 * (x * 40 - t * 2 * 3.141).sin",
"start": [
6,
1
],
"end": [
7,
80
],
"kind": "commanddeclaration"
},
{
"full_name": "Plot",
"code"... |
.lake/packages/proofwidgets/ProofWidgets/Demos/InteractiveSvg.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/InteractiveSvg.lean"
] | [
{
"full_name": "State",
"code": "abbrev State := Array (Float Γ Float)",
"start": [
7,
1
],
"end": [
7,
38
],
"kind": "commanddeclaration"
},
{
"full_name": "isvg",
"code": "def isvg : InteractiveSvg State where\n init := #[(-0.5, -0.5), (0.5, -0.5), ... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Venn.lean | [
".lake/packages/proofwidgets/ProofWidgets/Component/PenroseDiagram.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean",
".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean",
".lake/packages/lean4/src/lean/Lean/Elab/Tactic.lean",
".lake/packages/lean4/src/lean/Init.lean",
".lake/... | [
{
"full_name": "Set",
"code": "def Set (Ξ± : Type u) := Ξ± β Prop",
"start": [
12,
1
],
"end": [
12,
33
],
"kind": "commanddeclaration"
},
{
"full_name": "Set.Mem",
"code": "protected def Mem (a : Ξ±) (s : Set Ξ±) : Prop :=\n s a",
"start": [
16... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Euclidean.lean | [
".lake/packages/proofwidgets/ProofWidgets/Component/PenroseDiagram.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean",
".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean",
".lake/packages/lean4/src/lean/Lean... | [
{
"full_name": "IncidenceGeometry",
"code": "class IncidenceGeometry where\n Point : Type uβ\n Line : Type uβ\n Circle : Type uβ\n\n between : Point β Point β Point β Prop onLine : Point β Line β Prop\n onCircle : Point β Circle β Prop\n inCircle : Point β Circle β Prop\n centerCircle : Point β Circl... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Rubiks.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean"
] | [
{
"full_name": "RubiksProps",
"code": "structure RubiksProps where\n seq : Array String := #[]\n deriving ToJson, FromJson, Inhabited",
"start": [
6,
1
],
"end": [
8,
39
],
"kind": "commanddeclaration"
},
{
"full_name": "Rubiks",
"code": "@[widget_mo... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Macro.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean"
] | [
{
"full_name": "Lean.SourceInfo.mkCanonical",
"code": "def Lean.SourceInfo.mkCanonical : SourceInfo β SourceInfo\n | .synthetic s e _ => .synthetic s e true\n | si => si",
"start": [
13,
1
],
"end": [
15,
13
],
"kind": "commanddeclaration"
},
{
"full_nam... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Jsx.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean"
] | [
{
"full_name": "htmlLetters",
"code": "def htmlLetters : Array ProofWidgets.Html := #[\n <span style={json% {color: \"red\"}}>H</span>,\n <span style={json% {color: \"yellow\"}}>T</span>,\n <span style={json% {color: \"green\"}}>M</span>,\n <span style={json% {color: \"blue\"}}>L</span>\n ]",
... |
.lake/packages/proofwidgets/ProofWidgets/Demos/LazyComputation.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/Basic.lean"
] | [
{
"full_name": "MetaMStringCont",
"code": "structure MetaMStringCont where\n ci : Elab.ContextInfo\n lctx : LocalContext\n k : MetaM String\n deriving TypeName",
"start": [
6,
1
],
"end": [
12,
20
],
"kind": "commanddeclaration"
},
{
"full_name": "Runn... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Dynkin.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean"
] | [
{
"full_name": "List.product",
"code": "def List.product : List Ξ± β List Ξ² β List (Ξ± Γ Ξ²)\n | [], _ => []\n | a::as, bs => bs.map ((a, Β·)) ++ as.product bs",
"start": [
6,
1
],
"end": [
8,
50
],
"kind": "commanddeclaration"
},
{
"full_name": "Matrix"... |
.lake/packages/proofwidgets/ProofWidgets/Demos/ExprPresentation.lean | [
".lake/packages/proofwidgets/ProofWidgets/Component/Panel/SelectionPanel.lean",
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/Panel/GoalTypePanel.lean"
] | [
{
"full_name": "presenter",
"code": "@[expr_presenter]\ndef presenter : ExprPresenter where\n userName := \"With octopodes\"\n layoutKind := .inline\n present e :=\n return <span>\n {.text \"π \"}<InteractiveCode fmt={β Lean.Widget.ppExprTagged e} />{.text \" π\"}\n </span>",
"start"... |
.lake/packages/proofwidgets/ProofWidgets/Demos/RbTree.lean | [
".lake/packages/proofwidgets/ProofWidgets/Component/Panel/SelectionPanel.lean",
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Presentation/Expr.lean"
] | [
{
"full_name": "RBColour",
"code": "inductive RBColour where\n | red | black",
"start": [
7,
1
],
"end": [
8,
16
],
"kind": "commanddeclaration"
},
{
"full_name": "RBTree",
"code": "inductive RBTree (Ξ± : Type u) where\n | empty : RBTree Ξ±\n | node (... |
.lake/packages/proofwidgets/ProofWidgets/Demos/Svg.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean",
".lake/packages/proofwidgets/ProofWidgets/Data/Svg.lean"
] | [
{
"full_name": "frame",
"code": "private def frame : Frame where\n xmin := -2\n ymin := -2\n xSize := 4\n width := 400\n height := 400",
"start": [
6,
1
],
"end": [
11,
16
],
"kind": "commanddeclaration"
},
{
"full_name": "svg",
"code": "pri... |
.lake/packages/lean4/src/lean/Lean/Compiler/IR/EmitLLVM.lean | [
".lake/packages/lean4/src/lean/Lean/Compiler/ExportAttr.lean",
".lake/packages/lean4/src/lean/Lean/Runtime.lean",
".lake/packages/lean4/src/lean/Lean/Compiler/IR/EmitUtil.lean",
".lake/packages/lean4/src/lean/Lean/Compiler/IR/ResetReuse.lean",
".lake/packages/lean4/src/lean/Lean/Compiler/IR/Boxing.lean",
... | [
{
"full_name": "Lean.IR.leanMainFn",
"code": "def leanMainFn := \"_lean_main\"",
"start": [
24,
1
],
"end": [
24,
31
],
"kind": "commanddeclaration"
},
{
"full_name": "Lean.IR.LLVM.size_tType",
"code": "def size_tType (llvmctx : LLVM.Context) : BaseIO ... |
.lake/packages/lean4/src/lean/lake/Lake/Main.lean | [
".lake/packages/lean4/src/lean/Init.lean",
".lake/packages/lean4/src/lean/lake/Lake/CLI.lean",
".lake/packages/lean4/src/lean/lake/Lake.lean"
] | [
{
"full_name": "main",
"code": "def main (args : List String) : IO UInt32 := do\n Lake.cli args",
"start": [
9,
1
],
"end": [
10,
16
],
"kind": "commanddeclaration"
}
] |
.lake/packages/lean4/src/lean/Lean/Compiler/LCNF/Probing.lean | [
".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/ForEachExpr.lean",
".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/CompilerM.lean",
".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/PassManager.lean",
".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/PhaseExt.lean"
] | [
{
"full_name": "Lean.Compiler.LCNF.Probe",
"code": "abbrev Probe Ξ± Ξ² := Array Ξ± β CompilerM (Array Ξ²)",
"start": [
14,
1
],
"end": [
14,
50
],
"kind": "commanddeclaration"
},
{
"full_name": "Lean.Compiler.LCNF.Probe.map",
"code": "@[inline]\ndef map (f... |
.lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp.lean | [
".lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp/Basic.lean",
".lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp/Transform.lean"
] | [] |
.lake/packages/lean4/src/lean/Lean/Meta/Match/MVarRenaming.lean | [
".lake/packages/lean4/src/lean/Lean/Util/ReplaceExpr.lean"
] | [
{
"full_name": "Lean.Meta.MVarRenaming",
"code": "structure MVarRenaming where\n map : MVarIdMap MVarId := {}",
"start": [
11,
1
],
"end": [
13,
31
],
"kind": "commanddeclaration"
},
{
"full_name": "Lean.Meta.MVarRenaming.isEmpty",
"code": "def MVarRe... |
.lake/packages/lean4/src/lean/Lean/Data/Lsp/Window.lean | [
".lake/packages/lean4/src/lean/Lean/Data/Json.lean"
] | [
{
"full_name": "MessageType",
"code": "inductive MessageType where\n | error\n | warning\n | info\n | log",
"start": [
11,
1
],
"end": [
15,
8
],
"kind": "commanddeclaration"
},
{
"full_name": "ShowMessageParams",
"code": "structure ShowMessagePara... |
.lake/packages/lean4/src/lean/Std.lean | [
".lake/packages/lean4/src/lean/Init.lean"
] | [] |
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