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

theorem
  tanh.(p+r) = (tanh.p + tanh.r)/(1+ (tanh.p)*(tanh.r)) & tanh.(p-r) = (
  tanh.p - tanh.r)/(1- (tanh.p)*(tanh.r)) by Lm5,Lm9;
