  It is well known in the Constraint Programming community that any non-binary
constraint satisfaction problem (with finite domains) can be transformed into
an equivalent binary one. One of the most well-known translations is the Hidden
Variable Encoding. In this paper we formalize this encoding in the proof
assistant Coq and prove that any solution of the binary constraint satisfaction
problem makes it possible to build a solution of the original problem and
vice-versa. This formal development is used to complete the formally verified
constraint solver developed in Coq by Carlier, Dubois and Gotlieb in 2012,
making it a tool able to solve any n-ary constraint satisfaction problem, The
key of success of the connection between the translator and the Coq binary
solver is the genericity of the latter.
