Prenex Implicits mxmodule_form mxnonsimple_form mxnonsimple_sat.
(* Change of representation field (by tensoring) *)
Section ChangeOfField.
Variables (aF rF : fieldType) (f : {rmorphism aF -> rF}).
Local Notation "A ^f" := (map_mx (GRing.RMorphism.apply f) A) : ring_scope.
Variables (gT : finGroupType) (G : {group gT}).
Section OneRepresentation.
Variables (n : nat) (rG : mx_representation aF G n).
Local Notation rGf := (map_repr f rG).

Lemma map_section_repr n (rG : mx_representation aF G n) rGf U V
(modU : mxmodule rG U) (modV : mxmodule rG V)
(modUf : mxmodule rGf U^f) (modVf : mxmodule rGf V^f) :
map_repr f rG =1 rGf ->
mx_rsim (map_repr f (section_repr modU modV)) (section_repr modUf modVf).