proposition: Lemma unit_Bezout_mx m a b (k : 'I_m) : Bezout_mx a b k \in unitmx.
proof: Proof. rewrite /Bezout_mx; case:egcdrP=> g a1 b1 u v Huv Hg Ha1 Hb1. have H: a1 * u - b1 * -v = 1; first by rewrite mulrN opprK. by case: (mulmx1_unit (combine_mx_inv k H)). 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