Real tree and hyperbolicity 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?

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.
