(* Definition of log R+* -> R *)
(* Extension on R *)
Definition ln (x:R) : R :=
match Rlt_dec 0 x with
| left a => Rln (mkposreal x a)
| right a => 0
end.
Definition Rlog x y := (ln y)/(ln x).

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(** *                     Properties of  Ln                       *)
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Theorem ln_increasing : forall x y:R, 0 < x -> x < y -> ln x < ln y.