Watermarking techniques are used to help identifying copies of publicly released information. They consist in applying a slight and secret modification to the data before its release, in a way that should be robust, i.e. remain recognizable even in (reasonably) modified copies of the data. In this paper, we present new results about the robustness of watermarking schemes against arbitrary attackers, and the formalization of those results in \coq. We used the \alea library, which formalizes probability theory and models probabilistic programs using a simple monadic translation. This work illustrates the strengths and particularities of the induced style of reasoning about probabilistic programs. Our technique for proving robustness is adapted from methods commonly used for cryptographic protocols, and we discuss its relevance to the field of watermarking.