let E be set ; :: thesis: for A, B being Subset of (E ^omega) holds (A /\ B) * c= (A *) /\ (B *)
let A, B be Subset of (E ^omega); :: thesis: (A /\ B) * c= (A *) /\ (B *)
( (A /\ B) * c= A * & (A /\ B) * c= B * ) by Th61, XBOOLE_1:17;
hence (A /\ B) * c= (A *) /\ (B *) by XBOOLE_1:19; :: thesis: verum