theorem
  for D being non zero Integer holds
  { [x,y,z] where x,y,z is positive Nat : x^2-D*y^2 = z^2 & x,y are_coprime }
  is infinite
  proof
    let D be non zero Integer;
    D is odd or D is even;
    hence thesis by Lm11,Lm12;
  end;
