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

theorem Th17:
  for z being Complex holds sinh_C/.(<i>*z) = <i>*sin_C/.z
proof
  let z be Complex;
  reconsider z as Element of COMPLEX by XCMPLX_0:def 2;
  sinh_C/.(<i>*z) = (exp(<i>*z)-exp(-<i>*z))/2 by Def3
    .= <i>*((exp(<i>*z)-exp(-<i>*z))/(<i>*2));
  then sinh_C/.(<i>*z) = <i>*sin_C/.z by Def1;
  hence thesis;
end;
