Metric 20260629

theories/measure_theory/measurable_function.v

@@ -1,11 +1,10 @@
 (* mathcomp analysis (c) 2026 Inria and AIST. License: CeCILL-C.              *)
 From HB Require Import structures.
-From mathcomp Require Import all_ssreflect_compat algebra.
+From mathcomp Require Import all_ssreflect_compat.
 #[warning="-warn-library-file-internal-analysis"]
 From mathcomp Require Import unstable.
-From mathcomp Require Import boolp classical_sets functions cardinality reals.
-From mathcomp Require Import ereal topology normedtype.
-From mathcomp Require Import sequences measurable_structure.
+From mathcomp Require Import boolp classical_sets functions.
+From mathcomp Require Import measurable_structure.
 
 (**md**************************************************************************)
 (* # Measurable Functions                                                     *)
@@ -29,7 +28,6 @@ Set Implicit Arguments.
 Unset Strict Implicit.
 Unset Printing Implicit Defensive.
 Import ProperNotations.
-Import Order.TTheory GRing.Theory Num.Theory.
 
 Local Open Scope classical_set_scope.
 Local Open Scope ring_scope.
@@ -358,7 +356,7 @@ Context {d} {T : measurableType d} {d1} {T1 : measurableType d1}
 
 Lemma g_sigma_algebra_preimage_comp (X : {mfun T >-> T1}) (f : T1 -> T2) :
   measurable_fun [set: T1] f ->
-  g_sigma_algebra_preimage (f \o X)%R `<=` g_sigma_algebra_preimage X.
+  g_sigma_algebra_preimage (f \o X) `<=` g_sigma_algebra_preimage X.
 Proof. exact: preimage_set_system_compS. Qed.
 
 End g_sigma_algebra_preimage_comp.

theories/normedtype_theory/matrix_normedtype.v

@@ -251,6 +251,9 @@ HB.instance Definition _ (K : numFieldType) m n :=
   PseudoMetricNormedZmod_Lmodule_isNormedModule.Build K 'M[K]_(m, n)
     (@mx_normZ K m n).
 
+HB.instance Definition _ (K : numFieldType) m n :=
+  isNormedModule.Build _ 'M[K]_(m, n).
+
 End matrix_NormedModule.
 
 Lemma continuous_mx {V : topologicalType} {R : realFieldType} {m n : nat}

theories/normedtype_theory/normed_module.v

@@ -92,11 +92,33 @@ HB.mixin Record PseudoMetricNormedZmod_ConvexTvs_isNormedModule K V
   normrZ : forall (l : K) (x : V), `| l *: x | = `| l | * `| x |;
 }.
 
-#[short(type="normedModType")]
-HB.structure Definition NormedModule (K : numDomainType) :=
+HB.structure Definition NormedModule0 (K : numDomainType) :=
   {T of PseudoMetricNormedZmod K T & ConvexTvs K T
    & PseudoMetricNormedZmod_ConvexTvs_isNormedModule K T}.
 
+#[short(type="normedModType")]
+HB.structure Definition NormedModule (K : numDomainType) :=
+  {T of NormedModule0 K T & Metric K T}.
+
+HB.factory Record isNormedModule (K : numDomainType) T & NormedModule0 K T := { }.
+
+HB.builders Context K T & isNormedModule K T.
+
+Let mdist (x y : T) : K := `|x - y|.
+
+Let mdist_ge0 x y : 0 <= mdist x y. Proof. by rewrite /mdist. Qed.
+
+Let mdist_positivity x y : mdist x y = 0 -> x = y.
+Proof. by move=> /normr0_eq0/subr0_eq. Qed.
+
+Let ballEmdist x d : ball x d = [set y | mdist x y < d].
+Proof. by rewrite -ball_normE. Qed.
+
+HB.instance Definition _ :=
+  @PseudoMetric_isMetric.Build K T mdist mdist_ge0 mdist_positivity ballEmdist.
+
+HB.end.
+
 #[short(type="subNormedModType")]
 HB.structure Definition SubNormedModule (R : numDomainType)
   (V : normedModType R) (S : pred V) :=
@@ -1721,7 +1743,7 @@ Qed.
 Section prod_NormedModule.
 Context {K : numFieldType} {U V : normedModType K}.
 
-Lemma prod_norm_scale (l : K) (x : U * V) : `| l *: x | = `|l| * `| x |.
+Let prod_norm_scale (l : K) (x : U * V) : `| l *: x | = `|l| * `| x |.
 Proof. by rewrite prod_normE /= !normrZ maxr_pMr. Qed.
 
 HB.instance Definition _ :=
@@ -1730,6 +1752,9 @@ HB.instance Definition _ :=
 
 End prod_NormedModule.
 
+HB.instance Definition _ (R : numFieldType) (U V' : normedModType R) :=
+  isNormedModule.Build _ (U * V')%type.
+
 Section prod_NormedModule_lemmas.
 Context {T : Type} {K : numDomainType} {U V : normedModType K}.
 
@@ -2657,6 +2682,9 @@ HB.instance Definition _ (V : vectType R) :=
   PseudoMetricNormedZmod_Lmodule_isNormedModule.Build R (max_space V)
     (@Norm.normZ _ _ (@max_norm V)).
 
+HB.instance Definition _ (V : vectType R) :=
+  isNormedModule.Build _ (max_space V).
+
 (* NB: Get Trocq to prove the continuity part automatically. *)
 Lemma sup_closed_ball_compact (V : vectType R) :
   compact (closed_ball (0 : max_space V) 1).