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

theorem Th18:
  for z being Complex holds cosh_C/.(<i>*z) = cos_C/.z
proof
  let z be Complex;
  reconsider z as Element of COMPLEX by XCMPLX_0:def 2;
  cosh_C/.(<i>*z) = (exp(<i>*z) + exp(-<i>*z))/2 by Def4;
  then cosh_C/.(<i>*z) = cos_C/.z by Def2;
  hence thesis;
end;
