
theorem Th23:
  2 is_quadratic_non_residue_mod 3
proof
  now assume ex x being Integer st x|^2, 2 are_congruent_mod 3;
  then consider x being Integer such that
A1: x|^2,2 are_congruent_mod 3;
  now per cases by Th15;
  case x|^2, 0 are_congruent_mod 3;
    hence contradiction by A1,Th14;
    end;
  case x|^2, 1 are_congruent_mod 3;
    hence contradiction by A1,Th14;
    end;
  end;
  hence contradiction;
  end;
  hence thesis by Th22;
end;
