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 Th36:
  not x in omega implies x = [numerator x, denominator x] & denominator x <> 1
proof
  assume
A1: not x in omega;
  then consider i,j such that
A2: x = [i,j] and
  i,j are_coprime and
  j <> {} and
A3: j <> 1 by Th29;
  i = numerator x by A1,A2,Def8;
  hence thesis by A1,A2,A3,Def9;
end;
