proposition: Lemma index_pivot x s1 s2 (s := s1 ++ x :: s2) : x \notin s1 -> index x s = size s1.
proof: Proof. by rewrite index_cat/= eqxx addn0; case: ifPn. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)