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test subNormedZmodType #1928

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16 changes: 16 additions & 0 deletions theories/normedtype_theory/pseudometric_normed_Zmodule.v
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Expand Up @@ -143,6 +143,22 @@ HB.structure Definition PseudoMetricNormedZmod (R : numDomainType) :=
{T of Num.NormedZmodule R T & PseudoMetric R T
& NormedZmod_PseudoMetric_eq R T & isPointed T}.

HB.mixin Record Zmodule_isSubSemiNormed (R : numDomainType)
(M : semiNormedZmodType R) (S : pred M) T & SubType M S T
& Num.NormedZmodule R T := {
norm_valE : @Num.norm _ M \o (val : T -> M) = @Num.norm _ T
}.

#[short(type="subSemiNormedZmodType")]
HB.structure Definition SubSemiNormedZmodule (R : numDomainType)
(V : semiNormedZmodType R) (S : pred V) :=
{ W of GRing.SubZmodule V S W & Zmodule_isSubSemiNormed R V S W}.

#[short(type="subNormedZmodType")]
HB.structure Definition SubNormedZmodule (R : numDomainType)
(V : normedZmodType R) (S : pred V) :=
{ U of SubChoice V S U & Num.NormedZmodule R U & @SubSemiNormedZmodule R V S U }.

(* alternative definition of a PseudoMetricNormedZmod *)
HB.factory Record NormedZmoduleMetric (R : numDomainType) T
& Num.NormedZmodule R T & Metric R T & isPointed T := {
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