proposition: Lemma setIt_P (I:Set) (f:I-> Set): nonempty I -> forall x, (inc x (intersectiont f) <-> (forall j, inc x (f j))).
proof: Proof. move=> [i [ix _]];split; first by move /Zo_hi. move => h1; apply: Zo_i => //; apply /setUt_P; exists ix; apply: (h1 ix). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)