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 Th35:
  denominator x <> {}
proof
  per cases;
  suppose
    x in omega;
    hence thesis by Def9,Lm4;
  end;
  suppose
A1: not x in omega;
    then ex i,j st x = [i,j] & i,j are_coprime & j <> {} & j <> 1 by
Th29;
    hence thesis by A1,Def9;
  end;
end;
