  Capitalizing on previous encodings and formal developments about nominal
calculi and type systems, we propose a weak Higher-Order Abstract Syntax
formalization of the type language of pure System F<: within Coq, a proof
assistant based on the Calculus of Inductive Constructions.
  Our encoding allows us to accomplish the proof of the transitivity property
of algorithmic subtyping, which is in fact the first of the three tasks stated
by the POPLmark Challenge, a set of problems that capture the most critical
issues in formalizing programming language metatheory.
