reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;
reserve fi,psi for Ordinal-Sequence;

theorem Th33:
  A c= B implies C +^ A c= C +^ B
proof
  assume
A1: A c= B;
  now
    assume A <> B;
    then A c< B by A1;
    then C +^ A in C +^ B by Th32,ORDINAL1:11;
    hence thesis by ORDINAL1:def 2;
  end;
  hence thesis;
end;
