proposition: Lemma nonemptyP x: nonempty x <-> (x <> emptyset).
proof: Proof. split => xne; last by case: (emptyset_dichot x) => // ->. move => xe; case: xne; rewrite xe; exact:in_set0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)