inf_ov: forall p q, ov p q -> ov p (inf QDBool (bool_family _ p q))
properness: ov zero zero -> False;
distributivity: forall I p q, id _ (inf QDBool (bool_family _ (sup I p) q)) (sup I (fun i => (inf QDBool (bool_family _ (p i) q))));
inf_ov: forall p q, ov p q -> ov p (inf QDBool (bool_family _ p q))
properness: ov zero zero -> False;
distributivity: forall I p q, id _ (inf QDBool (bool_family _ (sup I p) q)) (sup I (fun i => (inf QDBool (bool_family _ (p i) q))));