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

theorem
  cosh.(p+r)=(cosh.p)*(cosh.r) + (sinh.p)*(sinh.r) & cosh.(p-r)=(cosh.p)
  *(cosh.r) - (sinh.p)*(sinh.r) by Lm2,Lm7;
