proposition: Lemma index_cat x s1 s2 : index x (s1 ++ s2) = if x \in s1 then index x s1 else size s1 + index x s2.
proof: Proof. by rewrite /index find_cat has_pred1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)