reserve p,q,r,th,th1 for Real;
reserve n for Nat;

theorem Th17:
  tanh.p = (sinh.p)/(cosh.p)
proof
  (sinh.p)/(cosh.p) =((exp_R.(p) - exp_R.(-p))/2)/(cosh.p) by Def1
    .=((exp_R.(p) - exp_R.(-p))/2)/((exp_R.(p) + exp_R.(-p))/2) by Def3
    .=(exp_R.(p) - exp_R.(-p))/(exp_R.(p) + exp_R.(-p)) by XCMPLX_1:55
    .=tanh.p by Def5;
  hence thesis;
end;
