theorem Th38:
  omega in W implies ex b,M st a in b & M = Rank b & M <==> W
proof
  assume omega in W;
  then consider b,M such that
A1: a in b & M = Rank b & M is_elementary_subsystem_of W by Th34;
  take b,M;
  thus thesis by A1,Th9;
end;
