(** * C is a NormedModule *)
Canonical C_UniformSpace :=
UniformSpace.Pack C (UniformSpace.class (prod_UniformSpace _ _)) C.
(** on C (with the balls of R^2) *)
Canonical C_ModuleSpace :=
ModuleSpace.Pack C_Ring C (ModuleSpace.class _ (Ring_ModuleSpace C_Ring)) C.
Canonical C_NormedModuleAux :=
NormedModuleAux.Pack C_AbsRing C (NormedModuleAux.Class C_AbsRing _ (ModuleSpace.class _ C_ModuleSpace) (UniformSpace.class C_UniformSpace)) C.

(* Specifications: *)
Lemma C_NormedModule_mixin_compat1 :
forall (x y : C) (eps : R),
Cmod (minus y x) < eps -> ball x eps y.
Lemma C_NormedModule_mixin_compat2 :
forall (x y : C_NormedModuleAux) (eps : posreal),
ball x eps y -> Cmod (minus y x) < sqrt 2 * eps.