
theorem
  for L being up-complete sup-Semilattice for D being non empty directed
  Subset of L, x being Element of L holds ex_sup_of {x} "\/" D,L
proof
  let L be up-complete sup-Semilattice, D be non empty directed Subset of L, x
  be Element of L;
  reconsider xx = {x} as non empty directed Subset of L by WAYBEL_0:5;
  ex_sup_of xx "\/" D,L by WAYBEL_0:75;
  hence thesis;
end;
