In contrast to other methods to bind variables, the nominal approach uses atoms and the algebra of atom permutations bringing enlightening implications. This talk will discuss the lessons learned from our experience towards formalising nominal matching and nominal unification modulo C and AC using the proof assistant PVS (Prototype Verification System). Furthermore, the talk will dissect exciting issues that appear during the formalisation of nominal equational reasoning giving rise to surprises regarding the well-known properties of first-order unification and unification modulo C and AC.