proposition: Lemma ker_mod1 m0 m1 (M : 'M[R]_(m0,m1)) : M %| M.-ker 1%:M.
proof: Proof. rewrite -dvdNmx; apply/dvdmxP; exists (lsubmx (ker (col_mx M 1%:M))). apply/eqP; rewrite mulmxN -addr_eq0 addrC -[M.-ker _]mulmx1 -mul_row_col. by rewrite hsubmxK kerK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq path) mathcomp(ssralg fintype perm choice matrix bigop zmodp mxalgebra poly) ssrcomplements dvdring stronglydiscrete