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

theorem Th15:
  cosh.p <> 0 & cosh.p > 0 & cosh.0 = 1
proof
  exp_R.p > 0 & exp_R.(-p) > 0 by SIN_COS:54;
  then
A1: (exp_R.p+exp_R.(-p))/2 > 0 by XREAL_1:139;
  cosh.0 = (exp_R.0+exp_R.(-0))/2 by Def3
    .= 1 by SIN_COS:51,def 23;
  hence thesis by A1,Def3;
end;
