proposition: Lemma domain_set0P x: nonempty (domain x) <-> nonempty x.
proof: Proof. split; last by move => h; apply:funI_setne. by move/nonemptyP => h; apply /nonemptyP; dneg xx; apply/domain_set0_P. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)