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

theorem Th3:
  for z being Complex holds cos_C/.z = cos_C/.(-z)
proof
  let z be Complex;
  reconsider z as Element of COMPLEX by XCMPLX_0:def 2;
  cos_C/.(-z) = (exp(<i>*(-z)) + exp(-<i>*(-z)))/2 by Def2
    .=(exp(-<i>*z) + exp(<i>*z))/2;
  then cos_C/.z = cos_C/.(-z) by Def2;
  hence thesis;
end;
