theorem
  for D being Integer holds
  { [x,y,z] where x,y,z is positive Nat : x^2-D*y^2 = z^2 } is infinite
  proof
    let D be Integer;
    D < 0 or D = 0 or D > 0;
    hence thesis by Lm52,Lm53,Lm54;
  end;
