proposition: Lemma setP_1 x: \Po (singleton x) = doubleton emptyset (singleton x).
proof: Proof. set_extens t. by move /setP_P /subset1P => [] ->; apply/set2_P; [left | right]. case /set2_P => ->; fprops; apply /setP_P; fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)