proposition: Lemma setU1E (x : T) (S : {set T}) : (x \in S) = (x |: S == S).
proof: Proof. apply/idP/eqP => [Hx | <-]; last by rewrite in_setU1 eqxx. apply/setP => y; rewrite in_setU1 orbC. by case: (boolP (y \in S)) => //= /negP; apply contra_notF => /eqP ->. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype fintype choice seq) mathcomp(finset bigop path binomial)