proposition: Lemma setId2P x pA pB pC : reflect [/\ pA x, pB x & pC x] (x \in [set y | pA y & pB y && pC y]).
proof: Proof. by rewrite !inE; apply: and3P. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)