  Proof by coupling is a classical proof technique for establishing
probabilistic properties of two probabilistic processes, like stochastic
dominance and rapid mixing of Markov chains. More recently, couplings have been
investigated as a useful abstraction for formal reasoning about relational
properties of probabilistic programs, in particular for modeling
reduction-based cryptographic proofs and for verifying differential privacy. In
this paper, we demonstrate that probabilistic couplings can be used for
verifying non-relational probabilistic properties. Specifically, we show that
the program logic pRHL---whose proofs are formal versions of proofs by
coupling---can be used for formalizing uniformity and probabilistic
independence. We formally verify our main examples using the EasyCrypt proof
assistant.
