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

Lemma archimed_cor1 :
forall eps:R, 0 < eps ->  exists N : nat, / INR N < eps /\ (0 < N)%nat.