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(** * Definition of hyperbolic functions *)
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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.

(* Specifications: *)
Lemma cosh_0 : cosh 0 = 1.
Lemma sinh_0 : sinh 0 = 0.