reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;
reserve U1,U2,U for Universe;

theorem Th54:
  U1,U2 are_c=-comparable
proof
A1: On U1 c= On U2 or On U2 c= On U1;
A2: U2 = Rank On U2 by Th50;
  U1 = Rank On U1 by Th50;
  hence U1 c= U2 or U2 c= U1 by A1,A2,CLASSES1:37;
end;
