proposition: Lemma size_v12 (r1_leq_r0 : size r1 <= size r0) : r1 != 0 -> size (v 1) <= size (v 2).
proof: Proof. move=> r10. rewrite /= /Euclid.v1 /Euclid.v0 addr0 mulr1 size_opp. rewrite size_divp // -subn1 subnBA ?lt0n ?size_poly_eq0 // size_poly1. by rewrite addnC -addnBA. Qed.
imports: mathcomp(all_ssreflect ssralg poly polydiv matrix)