reserve x,y for Real;
reserve z,z1,z2 for Complex;
reserve n for Element of NAT;

theorem Th2:
  for z being Complex holds -sin_C/.z = sin_C/.(-z)
proof
  let z be Complex;
  sin_C/.(-z) = (exp(<i>*(-z)) - exp(-<i>*(-z)))/(2*<i>) by Def1
    .= -((exp(<i>*z) - exp(-<i>*z))/(2*<i>));
  then -sin_C/.z = sin_C/.(-z) by Def1;
  hence thesis;
end;
