Real tree and hyperbolicity

Question

I seek a proof of the following result due to Tits:

Theorem: A path-connected $0$-hyperbolic metric space is a real tree.

Do you know any proof or reference?

Answer 1

I finally found the result as Théorème 4.1 in Coornaert, Delzant and Papadopoulos' book Géométrie et théorie des groupes, les groupes hyperboliques de Gromov, where path-connected is replaced with geodesic; and in a document written by Steven N. Evans: Probability and Real Trees (theorem 3.40), where path-connected is replaced with connected.

Answer 2

Might this be what you are looking for?

J. Tits, A "theorem of Lie-Kolchin" for trees, Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, Academic Press, New York, 1977, pp. 377–388.