A graft or an intervertebral piece or cage designed to be inserted between two vertebrae, and an implant in the form of a staple, having two lateral branches designed to be inserted into the plates of the respective vertebrae to be immobilized and a central branch connecting these two lateral branches to each other. At least one lateral branch has at least one mobile portion, movable between an introduction position, in which this mobile portion is located in the extension of the rest of this lateral branch, and an anchoring position, in which this mobile portion protrudes laterally in relation to the rest of the lateral branch, and the implant has movement means allowing the mobile portion to move between the introduction and anchoring positions.
