(* Sub-, isomorphic, simple, semisimple and completely reducible modules.     *)
(* All these predicates are intuitionistic (since, e.g., testing simplicity   *)
(* requires a splitting algorithm fo r the mas field). They are all           *)
(* specialized to square matrices, to avoid spurrious height parameters.      *)
(* Module isomorphism is an intentional property in general, but it can be    *)
(* decided when one of the two modules is known to be simple.                 *)
Variant mx_iso (U V : 'M_n) : Prop :=
MxIso f of f \in unitmx & (U <= dom_hom_mx f)%MS & (U *m f :=: V)%MS.

Lemma eqmx_iso U V : (U :=: V)%MS -> mx_iso U V.