  Coinductive reasoning about infinitary structures such as streams is widely
applicable. However, practical frameworks for developing coinductive proofs and
finding reasoning principles that help structure such proofs remain a
challenge, especially in the context of machine-checked formalization.
  This paper gives a novel presentation of an equational theory for reasoning
about structures up to weak bisimulation. The theory is both compositional,
making it suitable for defining general-purpose lemmas, and also incremental,
meaning that the bisimulation can be created interactively. To prove the
theory's soundness, this paper also introduces generalized parameterized
coinduction, which addresses expressivity problems of earlier works and
provides a practical framework for coinductive reasoning. The paper presents
the resulting equational theory for streams, but the technique applies to other
structures too.
  All of the results in this paper have been proved in Coq, and the generalized
parameterized coinduction framework is available as a Coq library.
