diff --git a/Mathlib/Algebra/LinearRecurrence.lean b/Mathlib/Algebra/LinearRecurrence.lean index 6634b8b7951ff4..cbbc654009610a 100644 --- a/Mathlib/Algebra/LinearRecurrence.lean +++ b/Mathlib/Algebra/LinearRecurrence.lean @@ -8,6 +8,7 @@ module public import Mathlib.Algebra.Polynomial.Degree.Operations public import Mathlib.Algebra.Polynomial.Eval.Defs public import Mathlib.LinearAlgebra.Dimension.Constructions +public import Mathlib.Tactic.CrossRefAttribute /-! # Linear recurrence @@ -48,6 +49,7 @@ open Polynomial /-- A "linear recurrence relation" over a commutative semiring is given by its order `n` and `n` coefficients. -/ +@[wikidata Q364089] structure LinearRecurrence (R : Type*) [CommSemiring R] where /-- Order of the linear recurrence -/ order : β„• diff --git a/Mathlib/Analysis/InnerProductSpace/PiL2.lean b/Mathlib/Analysis/InnerProductSpace/PiL2.lean index 9836ea7f5a2ede..f915ca4763ad8d 100644 --- a/Mathlib/Analysis/InnerProductSpace/PiL2.lean +++ b/Mathlib/Analysis/InnerProductSpace/PiL2.lean @@ -10,6 +10,7 @@ public import Mathlib.Analysis.Normed.Lp.PiLp public import Mathlib.Analysis.Normed.Lp.Matrix public import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas public import Mathlib.LinearAlgebra.UnitaryGroup +public import Mathlib.Tactic.CrossRefAttribute public import Mathlib.Util.Superscript /-! @@ -108,6 +109,7 @@ space use `EuclideanSpace π•œ (Fin n)`. For the case when `n = Fin _`, there is `!β‚‚[x, y, ...]` notation for building elements of this type, analogous to `![x, y, ...]` notation. -/ +@[wikidata Q17295] abbrev EuclideanSpace (π•œ : Type*) (n : Type*) : Type _ := PiLp 2 fun _ : n => π•œ diff --git a/Mathlib/LinearAlgebra/Basis/Defs.lean b/Mathlib/LinearAlgebra/Basis/Defs.lean index c66920d1a2c6eb..c4ff6d939ed635 100644 --- a/Mathlib/LinearAlgebra/Basis/Defs.lean +++ b/Mathlib/LinearAlgebra/Basis/Defs.lean @@ -6,6 +6,7 @@ Authors: Johannes HΓΆlzl, Mario Carneiro, Alexander Bentkamp module public import Mathlib.LinearAlgebra.Finsupp.LinearCombination +public import Mathlib.Tactic.CrossRefAttribute /-! # Bases @@ -85,6 +86,7 @@ To turn a linear independent family of vectors spanning `M` into a basis, use `B They are internally represented as linear equivs `M ≃ₗ[R] (ΞΉ β†’β‚€ R)`, available as `Basis.repr`. -/ +@[wikidata Q189569] structure Basis where /-- `Basis.ofRepr` constructs a basis given an assignment of coordinates to each vector. -/ ofRepr :: diff --git a/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean b/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean index d6eb7a6bedd007..33ca6fe5da724c 100644 --- a/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean +++ b/Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean @@ -9,6 +9,7 @@ public import Mathlib.RingTheory.Congruence.Hom public import Mathlib.LinearAlgebra.TensorAlgebra.Basic public import Mathlib.LinearAlgebra.QuadraticForm.Isometry public import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv +public import Mathlib.Tactic.CrossRefAttribute /-! # Clifford Algebras @@ -69,6 +70,7 @@ end CliffordAlgebra /-- The Clifford algebra of an `R`-module `M` equipped with a `QuadraticForm` `Q`. -/ +@[wikidata Q674689] def CliffordAlgebra := CliffordAlgebra.ringCon Q |>.Quotient deriving Inhabited, Ring, Algebra R diff --git a/Mathlib/LinearAlgebra/Dual/Defs.lean b/Mathlib/LinearAlgebra/Dual/Defs.lean index 62a06d2c073886..0323991b305053 100644 --- a/Mathlib/LinearAlgebra/Dual/Defs.lean +++ b/Mathlib/LinearAlgebra/Dual/Defs.lean @@ -7,6 +7,7 @@ module public import Mathlib.LinearAlgebra.BilinearMap public import Mathlib.LinearAlgebra.Span.Defs +public import Mathlib.Tactic.CrossRefAttribute /-! # Dual vector spaces @@ -57,6 +58,7 @@ variable (R A M : Type*) variable [CommSemiring R] [AddCommMonoid M] [Module R M] /-- The left dual space of an R-module M is the R-module of linear maps `M β†’ R`. -/ +@[wikidata Q752487] abbrev Dual (R M : Type*) [Semiring R] [AddCommMonoid M] [Module R M] := M β†’β‚—[R] R diff --git a/Mathlib/LinearAlgebra/RootSystem/Defs.lean b/Mathlib/LinearAlgebra/RootSystem/Defs.lean index 1b5b341eac3111..3dd44ce2f78b71 100644 --- a/Mathlib/LinearAlgebra/RootSystem/Defs.lean +++ b/Mathlib/LinearAlgebra/RootSystem/Defs.lean @@ -7,6 +7,7 @@ module public import Mathlib.LinearAlgebra.PerfectPairing.Basic public import Mathlib.LinearAlgebra.Reflection +public import Mathlib.Tactic.CrossRefAttribute /-! # Root data and root systems @@ -113,6 +114,7 @@ variable {ΞΉ R M N} variable (P : RootPairing ΞΉ R M N) (i j : ΞΉ) /-- A root system is a root pairing for which the roots and coroots span their ambient modules. -/ +@[wikidata Q534131] class IsRootSystem : Prop where span_root_eq_top : span R (range P.root) = ⊀ span_coroot_eq_top : span R (range P.coroot) = ⊀ diff --git a/Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean b/Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean index fda5b38bd6fb45..6cfccad643f8bb 100644 --- a/Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean +++ b/Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean @@ -6,6 +6,7 @@ Authors: RΓ©my Degenne module public import Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1 +public import Mathlib.Tactic.CrossRefAttribute import Mathlib.MeasureTheory.Function.LpSpace.InfiniteSum @@ -97,6 +98,7 @@ It is defined as 0 if any one of the following conditions is true: - `m` is not a sub-Οƒ-algebra of `mβ‚€`, - `ΞΌ` is not Οƒ-finite with respect to `m`, - `f` is not integrable. -/ +@[wikidata Q772232] noncomputable irreducible_def condExp (ΞΌ : Measure[mβ‚€] Ξ±) (f : Ξ± β†’ E) : Ξ± β†’ E := if hm : m ≀ mβ‚€ then if h : SigmaFinite (ΞΌ.trim hm) ∧ Integrable f ΞΌ then diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/IntegrationByParts.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/IntegrationByParts.lean index 7e7ca233026342..358f01e9d06fb1 100644 --- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/IntegrationByParts.lean +++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/IntegrationByParts.lean @@ -7,6 +7,7 @@ module public import Mathlib.MeasureTheory.Function.JacobianOneDim public import Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus +public import Mathlib.Tactic.CrossRefAttribute /-! # Integration by parts and by substitution @@ -526,6 +527,7 @@ theorem integral_comp_mul_deriv' {f f' g : ℝ β†’ ℝ} (h : βˆ€ x ∈ uIcc a b, and `g` is continuous, then we can substitute `u = f x` to get `∫ x in a..b, (g ∘ f) x * f' x = ∫ u in f a..f b, g u`. -/ +@[wikidata Q1071270] theorem integral_comp_mul_deriv {f f' g : ℝ β†’ ℝ} (h : βˆ€ x ∈ uIcc a b, HasDerivAt f (f' x) x) (h' : ContinuousOn f' (uIcc a b)) (hg : Continuous g) : (∫ x in a..b, (g ∘ f) x * f' x) = ∫ x in f a..f b, g x := diff --git a/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean b/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean index 243d55e8c4436f..0fe73938b60340 100644 --- a/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean +++ b/Mathlib/MeasureTheory/Integral/IntervalIntegral/TrapezoidalRule.lean @@ -6,6 +6,7 @@ Authors: P. Michael Kielstra module public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic +public import Mathlib.Tactic.CrossRefAttribute public import Mathlib.Tactic.Field /-! @@ -29,6 +30,7 @@ open MeasureTheory intervalIntegral Interval Finset HasDerivWithinAt Set /-- Integration of `f` from `a` to `b` using the trapezoidal rule with `N+1` total evaluations of `f`. (Note the off-by-one problem here: `N` counts the number of trapezoids, not the number of evaluations.) -/ +@[wikidata Q833293] noncomputable def trapezoidal_integral (f : ℝ β†’ ℝ) (N : β„•) (a b : ℝ) : ℝ := ((b - a) / N) * ((f a + f b) / 2 + βˆ‘ k ∈ range (N - 1), f (a + (k + 1) * (b - a) / N)) diff --git a/Mathlib/NumberTheory/LSeries/RiemannZeta.lean b/Mathlib/NumberTheory/LSeries/RiemannZeta.lean index fdff2c94adcfd8..3c92195fce20df 100644 --- a/Mathlib/NumberTheory/LSeries/RiemannZeta.lean +++ b/Mathlib/NumberTheory/LSeries/RiemannZeta.lean @@ -117,6 +117,7 @@ lemma completedRiemannZeta_residue_one : -/ /-- The Riemann zeta function `ΞΆ(s)`. -/ +@[wikidata Q187235] def riemannZeta := hurwitzZetaEven 0 lemma HurwitzZeta.hurwitzZetaEven_zero : hurwitzZetaEven 0 = riemannZeta := rfl diff --git a/Mathlib/Order/Filter/Extr.lean b/Mathlib/Order/Filter/Extr.lean index 0c646f48feabca..f8337827d8f967 100644 --- a/Mathlib/Order/Filter/Extr.lean +++ b/Mathlib/Order/Filter/Extr.lean @@ -9,6 +9,7 @@ public import Mathlib.Order.Filter.Tendsto public import Mathlib.Order.ConditionallyCompleteLattice.Indexed public import Mathlib.Algebra.Order.Group.Defs public import Mathlib.Data.Finset.Lattice.Fold +public import Mathlib.Tactic.CrossRefAttribute /-! # Minimum and maximum w.r.t. a filter and on a set @@ -114,6 +115,7 @@ def IsMaxOn := IsMaxFilter f (π“Ÿ s) a /-- `IsExtrOn f s a` means `IsMinOn f s a` or `IsMaxOn f s a` -/ +@[wikidata Q845060] def IsExtrOn : Prop := IsExtrFilter f (π“Ÿ s) a diff --git a/Mathlib/RingTheory/LocalRing/ResidueField/Defs.lean b/Mathlib/RingTheory/LocalRing/ResidueField/Defs.lean index 5841aa7aa67bef..dd141c6c82a710 100644 --- a/Mathlib/RingTheory/LocalRing/ResidueField/Defs.lean +++ b/Mathlib/RingTheory/LocalRing/ResidueField/Defs.lean @@ -7,6 +7,7 @@ module public import Mathlib.RingTheory.Ideal.Quotient.Basic public import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic +public import Mathlib.Tactic.CrossRefAttribute /-! @@ -25,6 +26,7 @@ namespace IsLocalRing variable (R : Type*) [CommRing R] [IsLocalRing R] /-- The residue field of a local ring is the quotient of the ring by its maximal ideal. -/ +@[wikidata Q7315530] def ResidueField := R β§Έ maximalIdeal R deriving CommRing, Inhabited diff --git a/Mathlib/Topology/Algebra/Module/LocallyConvex.lean b/Mathlib/Topology/Algebra/Module/LocallyConvex.lean index c252b2838872f4..c73f0cfd0adb75 100644 --- a/Mathlib/Topology/Algebra/Module/LocallyConvex.lean +++ b/Mathlib/Topology/Algebra/Module/LocallyConvex.lean @@ -6,6 +6,7 @@ Authors: Anatole Dedecker module public import Mathlib.Analysis.Convex.Topology +public import Mathlib.Tactic.CrossRefAttribute public import Mathlib.Topology.Connected.LocallyPathConnected public import Mathlib.Analysis.Convex.PathConnected @@ -46,6 +47,7 @@ section Semimodule /-- A `LocallyConvexSpace` is a topological semimodule over an ordered semiring in which convex neighborhoods of a point form a neighborhood basis at that point. -/ +@[wikidata Q1572357] class LocallyConvexSpace (π•œ E : Type*) [Semiring π•œ] [PartialOrder π•œ] [AddCommMonoid E] [Module π•œ E] [TopologicalSpace E] : Prop where convex_basis : βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id diff --git a/Mathlib/Topology/UniformSpace/Cauchy.lean b/Mathlib/Topology/UniformSpace/Cauchy.lean index 343f98439c2ac3..74fd21c99e4b5b 100644 --- a/Mathlib/Topology/UniformSpace/Cauchy.lean +++ b/Mathlib/Topology/UniformSpace/Cauchy.lean @@ -5,6 +5,7 @@ Authors: Johannes HΓΆlzl, Mario Carneiro -/ module +public import Mathlib.Tactic.CrossRefAttribute public import Mathlib.Topology.Algebra.Constructions public import Mathlib.Topology.Bases public import Mathlib.Algebra.Order.Group.Nat @@ -365,6 +366,7 @@ theorem isComplete_iUnion_separated {ΞΉ : Sort*} {s : ΞΉ β†’ Set Ξ±} (hs : βˆ€ i /-- A complete space is defined here using uniformities. A uniform space is complete if every Cauchy filter converges. -/ +@[wikidata Q848569] class CompleteSpace (Ξ± : Type u) [UniformSpace Ξ±] : Prop where /-- In a complete uniform space, every Cauchy filter converges. -/ complete : βˆ€ {f : Filter Ξ±}, Cauchy f β†’ βˆƒ x, f ≀ 𝓝 x