  We introduce an infinitary first order linear logic with least and greatest
fixed points. To ensure cut elimination, we impose a validity condition on
infinite derivations. Our calculus is designed to reason about rich signatures
of mutually defined inductive and coinductive linear predicates. In a major
case study we use it to prove the strong progress property for binary
session-typed processes under an asynchronous communication semantics. As far
as we are aware, this is the first proof of this property.
