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

theorem
  (A^i) \/ (B^i) c= (A \/ B)^i
proof
  let x be object;
  assume
A1: x in (A^i) \/ (B^i);
  then reconsider px=x as Point of T;
  x in A^i or x in B^i by A1,XBOOLE_0:def 3;
  then
A2: U_FT px c= A or U_FT px c= B by FIN_TOPO:7;
  A c= A \/ B & B c= A \/ B by XBOOLE_1:7;
  then U_FT px c= A \/ B by A2;
  hence thesis by FIN_TOPO:7;
end;
