reserve X for set;
reserve UN for Universe;

theorem Th109:
  for n being Nat holds ComplUniverse.n is non empty
  proof
    let n be Nat;
    assume ComplUniverse.n is empty;
    then
A1: UNIVERSE (n + 1) \ UNIVERSE n = {} by Def14;
A2: UNIVERSE (n + 1) is axiom_GU1;
    UNIVERSE n in UNIVERSE (n + 1) by Th99;
    then UNIVERSE n c= UNIVERSE (n + 1) by A2;
    then UNIVERSE (n + 1) = UNIVERSE n by A1,XBOOLE_1:37;
    then n = n + 1 by CLASSES2:71;
    hence thesis;
  end;
