proposition: Lemma size_cut_k k s ss : ss \in (cut_k k s) -> size ss = k.
proof: Proof. Proof using. rewrite /cut_k => /mapP[sh /in_vect_n_k/andP[/eqP Hsum /eqP Hsize] -> {ss}]. by rewrite -(size_map size _) -/(shape _) reshapeKl; last rewrite Hsum. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype seq) tools