reserve T for non empty RelStr,
  A,B for Subset of T,
  x,x2,y,z for Element of T;

theorem Th12:
  (A^d) /\ (B^d) = (A /\ B)^d
proof
A1: B^d = ((B`)^f)` by Th4;
  thus (A^d) /\ (B^d) = (((A`)^f)`) /\ (B^d) by Th4
    .= (((A`)^f) \/ ((B`)^f))` by A1,XBOOLE_1:53
    .= ((A` \/ B`)^f)` by Th11
    .= (((A /\ B)`)^f)` by XBOOLE_1:54
    .= (A /\ B)^d by Th4;
end;
