proposition: Lemma mxrank_mul_min m n p (A : 'M_(m, n)) (B : 'M_(n, p)) : \rank A + \rank B - n <= \rank (A *m B).
proof: Proof. by have:= mxrank_Frobenius A 1%:M B; rewrite mulmx1 mul1mx mxrank1 leq_subLR. 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)