  We prove a conjecture about the constructibility of coinductive types - in
the principled form of indexed M-types - in Homotopy Type Theory. The
conjecture says that in the presence of inductive types, coinductive types are
derivable. Indeed, in this work, we construct coinductive types in a subsystem
of Homotopy Type Theory; this subsystem is given by Intensional Martin-L\"of
type theory with natural numbers and Voevodsky's Univalence Axiom. Our results
are mechanized in the computer proof assistant Agda.
