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).

(* Specifications: *)
Lemma map_rfix_mx H : (rfix_mx rG H)^f = rfix_mx rGf H.
Lemma rcent_map A : rcent rGf A^f = rcent rG A.
Lemma rstab_map m (U : 'M_(m, n)) : rstab rGf U^f = rstab rG U.
Lemma rstabs_map m (U : 'M_(m, n)) : rstabs rGf U^f = rstabs rG U.
Lemma mx_irr_map : mx_irreducible rGf -> mx_irreducible rG.
End OneRepresentation.
Lemma mx_rsim_map n1 n2 rG1 rG2 :
@mx_rsim _ _ G n1 rG1 n2 rG2 -> mx_rsim (map_repr f rG1) (map_repr f rG2).
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).
Lemma map_regular_subseries U i (modU : mx_subseries (regular_repr aF G) U)
(modUf : mx_subseries (regular_repr rF G) [seq M^f | M <- U]) :
mx_rsim (map_repr f (subseries_repr i modU)) (subseries_repr i modUf).
Lemma extend_group_splitting_field :
group_splitting_field aF G -> group_splitting_field rF G.