proposition: Lemma take_size_cat n s1 s2 : size s1 = n -> take n (s1 ++ s2) = s1.
proof: Proof. by move <-; elim: s1 => [|x s1 IHs]; rewrite ?take0 //= IHs. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)