
theorem Th1:
  for L being complete LATTICE, X,Y being set st X c= Y holds "\/"(
  X,L) <= "\/"(Y,L) & "/\"(X,L) >= "/\"(Y,L)
proof
  let L be complete LATTICE, X,Y be set;
A1: ex_inf_of X,L & ex_inf_of Y,L by YELLOW_0:17;
  ex_sup_of X,L & ex_sup_of Y,L by YELLOW_0:17;
  hence thesis by A1,YELLOW_0:34,35;
end;
