proposition: Lemma bigcap_setU_distr: forall (U T : Type) (s1 s2 : set U) (f : U -> set T), \bigcap_(i in s1) f i :&: \bigcap_(i in s2) f i <--> \bigcap_(i in s1 :|: s2) f i.
proof: Proof. intros. split. - intros [ H1 H2 ] x [ H3 | H3 ]; eauto. - intros H. split; intros x H3; eapply H. now left. now right. Qed.
imports: mathcomp.ssreflect.ssreflect Classes.RelationClasses Classes.Morphisms List Tactics mathcomp(ssrfun ssrbool ssrnat seq)