theorem Th3:
  -a*x = (-a)*x & -a*x = a*(-x)
proof
  thus -a*x = ((-1)*a)*x by EUCLID_4:4
    .= (-a)*x;
  hence -a*x = (a*(-1))*x .= a*(-x) by EUCLID_4:4;
end;
