proposition: Lemma partition_set_in_PP p E: partition_s p E -> inc p (\Po (\Po E)).
proof: Proof. by move=> [[<- _] _ ]; apply /setP_P => t ty;apply/setP_P; apply: setU_s1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)