theorem Th25:
  Lege (a,p) = 1 or Lege (a,p) = 0 or Lege (a,p) = -1
  proof
  per cases;
  suppose a is_quadratic_residue_mod p & a mod p <> 0;
    hence thesis by Def3;
  end;
  suppose a is_quadratic_residue_mod p & a mod p = 0;
    hence thesis by Def3;
  end;
  suppose not a is_quadratic_residue_mod p;
    hence thesis by Def3;
  end;
  end;
