proposition: Lemma dvdr_col_mx m n p x (M : 'M[R]_(m,n)) (N : 'M[R]_(p,n)) : (forall i j, x %| M i j) /\ (forall i j, x %| N i j) -> forall i j, x %| (col_mx M N) i j.
proof: Proof. case=> h1 h2 i j; rewrite !mxE; case: splitP=> k {i}_. exact: (h1 k j). exact: (h2 k j). Qed.
imports: HB(structures) Coq(ssreflect ssrfun ssrbool Arith.Wf_nat) mathcomp(eqtype ssrnat div seq path) mathcomp(ssralg fintype perm tuple choice generic_quotient) mathcomp(matrix bigop zmodp mxalgebra poly) stronglydiscrete