  Practical checkers based on refinement types use the combination of implicit
semantic sub-typing and parametric polymorphism to simplify the specification
and automate the verification of sophisticated properties of programs. However,
a formal meta-theoretic accounting of the soundness of refinement type systems
using this combination has proved elusive. We present \lambda_RF a core
refinement calculus that combines semantic sub-typing and parametric
polymorphism. We develop a meta-theory for this calculus and prove soundness of
the type system. Finally, we give a full mechanization of our meta-theory using
the refinement-type based LiquidHaskell as a proof checker, showing how
refinements can be used for mechanization.
