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Generalize prod_pseudoMetricNormedZmodType #232

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Merged
CohenCyril merged 1 commit into from
Aug 7, 2020
Merged

Generalize prod_pseudoMetricNormedZmodType #232

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21 changes: 13 additions & 8 deletions theories/normedtype.v
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Original file line number Diff line number Diff line change
Expand Up @@ -2656,11 +2656,8 @@ End matrix_NormedModule.

(** ** Pairs *)

Section prod_NormedModule.
Context {K : numDomainType} {U V : normedModType K}.

Lemma prod_norm_scale (l : K) (x : U * V) : `| l *: x | = `|l| * `| x |.
Proof. by rewrite prod_normE /= !normmZ maxr_pmulr. Qed.
Section prod_PseudoMetricNormedZmodule.
Context {K : numDomainType} {U V : pseudoMetricNormedZmodType K}.

Lemma ball_prod_normE : ball = ball_ (fun x => `| x : U * V |).
Proof.
Expand All @@ -2672,10 +2669,18 @@ Qed.
Lemma prod_norm_ball : @ball _ [pseudoMetricType K of U * V] = ball_ (fun x => `|x|).
Proof. by rewrite /= - ball_prod_normE. Qed.

Definition prod_PseudoMetricNormedZmodMixin :=
Definition prod_pseudoMetricNormedZmodMixin :=
PseudoMetricNormedZmodule.Mixin prod_norm_ball.
Canonical prod_topologicalZmodType :=
PseudoMetricNormedZmodType K (U * V) prod_PseudoMetricNormedZmodMixin.
Canonical prod_pseudoMetricNormedZmodType :=
PseudoMetricNormedZmodType K (U * V) prod_pseudoMetricNormedZmodMixin.

End prod_PseudoMetricNormedZmodule.

Section prod_NormedModule.
Context {K : numDomainType} {U V : normedModType K}.

Lemma prod_norm_scale (l : K) (x : U * V) : `| l *: x | = `|l| * `| x |.
Proof. by rewrite prod_normE /= !normmZ maxr_pmulr. Qed.

Definition prod_NormedModMixin := NormedModMixin prod_norm_scale.
Canonical prod_normedModType :=
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