Section MapMatrixSpaces.
Variables (aF rF : fieldType) (f : {rmorphism aF -> rF}).
Local Notation "A ^f" := (map_mx f A) : ring_scope.

Lemma map_submx m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
(A^f <= B^f)%MS = (A <= B)%MS.