(*****************************************)
(** * Definition of hyperbolic functions *)
(*****************************************)
Definition cosh (x:R) : R := (exp x + exp (- x)) / 2.Definition sinh (x:R) : R := (exp x - exp (- x)) / 2.Definition tanh (x:R) : R := sinh x / cosh x.

Lemma sinh_0 : sinh 0 = 0.