proposition: Lemma eqseq_cat s1 s2 s3 s4 : size s1 = size s2 -> (s1 ++ s3 == s2 ++ s4) = (s1 == s2) && (s3 == s4).
proof: Proof. elim: s1 s2 => [|x1 s1 IHs] [|x2 s2] //= [sz12]. by rewrite !eqseq_cons -andbA IHs. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)