proposition: Lemma setIt_sub2 (I:Set) (f: I-> Set) x: (forall i, sub (f i) x) -> sub (intersectiont f) x.
proof: Proof. move=> hyp t ti. case: (emptyset_dichot I) => ie. by move: ti; rewrite setIt_0 // => /in_set0. case: ie => y [ z _]; exact:(hyp z _ (setIt_s1 z ti)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)