proposition: Lemma map_eqmx m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : (A^f :=: B^f)%MS <-> (A :=: B)%MS.
proof: Proof. split=> [/eqmxP|eqAB]; first by rewrite !map_submx => /eqmxP. by apply/eqmxP; rewrite !map_submx !eqAB !submx_refl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg finalg zmodp matrix)