proposition: Lemma map_mx_inj {m n} : injective (map_mx f : 'M_(m, n) -> 'M_(m, n)).
proof: Proof. move=> A B eq_AB; apply/matrixP=> i j. by move/matrixP/(_ i j): eq_AB => /[!mxE]; apply: fmorph_inj. 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 countalg finalg zmodp)