proposition: Lemma vctleq_sumn_right_sizes t1 t2 : right_sizes t1 <=V right_sizes t2 -> sumn (right_sizes t1) <= sumn (right_sizes t2) ?= iff (t1 == t2).
proof: Proof. rewrite /vctleq -(inj_eq (can_inj right_sizesK)) => /andP[]. elim: (right_sizes t1) (right_sizes t2) => [| u0 u IHu] [| v0 v] //=. rewrite eqSS => {}/IHu Hrec /andP[H0 {}/Hrec] [Hleq Heq]. exact: leqif_add. Qed.
imports: HB(structures) mathcomp(all_ssreflect) tools combclass ordtype