reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;
reserve i,j,k for Element of omega;
reserve x,y,z for Element of RAT+;

theorem Th31:
  A in RAT+ implies A in omega
proof
  assume A in RAT+ & not A in omega;
  then ex i,j st A = [i,j] & i,j are_coprime & j <> {} & j <> 1 by Th29;
  hence thesis by Th30;
end;
