
theorem Th23:
  for L be Semilattice for x be Element of L holds x is
  completely-irreducible implies x is irreducible
proof
  let L be Semilattice;
  let x be Element of L;
  assume x is completely-irreducible;
  then
A1: x in Irr L by Def4;
  Irr L c= IRR L by Th22;
  hence thesis by A1,WAYBEL_6:def 4;
end;
