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 Th62, XBOOLE_1:17;
hence (A /\ B) * c= (A * ) /\ (B * ) by XBOOLE_1:19; :: thesis: verum