In mobile robotic swarms, the gathering problem consists in coordinating all the robots so that in finite time they occupy the same location, not known beforehand. Multiplicity detection refers to the ability to detect that more than one robot can occupy a given position. When the robotic swarm operates synchronously, a well-known result by Cohen and Peleg permits to achieve gathering, provided robots are capable of multiplicity detection. We present a new algorithm for synchronous gathering, that does not assume that robots are capable of multiplicity detection, nor make any other extra assumption. Unlike previous approaches, our proof correctness is certified in the model where the protocol is defined, using the Coq proof assistant.