proposition: Lemma bigcapP x P F : reflect (forall i, P i -> x \in F i) (x \in \bigcap_(i | P i) F i).
proof: Proof. rewrite -sub1set. by apply: (iffP (bigcapsP _ _ _)) => Fx i /Fx; rewrite sub1set. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)