proposition: Lemma mxrank_injP m n p (A : 'M_(m, n)) (f : 'M_(n, p)) : reflect (\rank (A *m f) = \rank A) ((A :&: kermx f)%MS == 0).
proof: Proof. rewrite -mxrank_eq0 -(eqn_add2l (\rank (A *m f))). by rewrite mxrank_mul_ker addn0 eq_sym; apply: eqP. 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)