proposition: Lemma imset0mem : (set0 \in fP) = (set0 \in P).
proof: Proof. apply/imsetP/idP => [[A AP /esym/eqP]|P0]; last by exists set0; rewrite ?imset0. by rewrite imset_eq0 => /eqP<-. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)