theorem Th59:
  (Omega).G "\/" H = (Omega).G & H "\/" (Omega).G = (Omega).G
proof
A1: (the carrier of (Omega). G) \/ carr H = [#] the carrier of G by SUBSET_1:11
;
  hence (Omega).G "\/" H = (Omega).G by Th31;
  thus thesis by A1,Th31;
end;
