The approach has two main ingredients: one is that of adopting relations as “first class citizens” in a pointfree reasoning style; the other lies on a synergy found between a relational construct, Reynolds’ relation on functions involved in the abstraction theorem on parametric polymorphism and the coalgebraic account of bisimulations and invariants. This leads to an elegant proof of the equivalence between two different definitions of bisimulation found in coalgebra literature (due to B. Jacobs and Aczel & Mendler, respectively) and to their instantiation to the classical Park-Milner definition popular in process algebra.