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

theorem Th15:
  for z being Complex holds sin_C/.(<i>*z) = <i>*sinh_C/.z
proof
  let z be Complex;
  reconsider z as Element of COMPLEX by XCMPLX_0:def 2;
  sin_C/.(<i>*z) = (exp(<i>*<i>*z) - exp(-<i>*(<i>*z)))/(<i>*2) by Def1
    .= <i>*((exp(z) - exp(-z))/2);
  then sin_C/.(<i>*z) = <i>*sinh_C/.z by Def3;
  hence thesis;
end;
