+(* subset top (full subset) *)
+definition stop \def \lambda (D:Domain). true_f D.
+
+(* subset bottom (empty subset) *)
+definition sbot \def \lambda (D:Domain). false_f D.
+
+(* subset and (binary intersection) *)
+definition sand: \forall D. Subset D \to Subset D \to Subset D \def
+ \lambda D,U1,U2,d. U1 d \land U2 d.
+
+(* subset or (binary union) *)
+definition sor: \forall D. Subset D \to Subset D \to Subset D \def
+ \lambda D,U1,U2,d. U1 d \lor U2 d.
+
+(* subset less or equal (inclusion) *)
+definition sle: \forall D. Subset D \to Subset D \to Prop \def
+ \lambda D,U1,U2. \iforall d. U1 d \to U2 d.