  We apply the foundational proof certificate (FPC) framework to the problem of
designing high-level outlines of proofs. The FPC framework provides a means to
formally define and check a wide range of proof evidence. A focused proof
system is central to this framework and such a proof system provides an
interesting approach to proof reconstruction during the process of proof
checking (relying on an underlying logic programming implementation). Here, we
illustrate how the FPC framework can be used to design proof outlines and then
to exploit proof checkers as a means for expanding outlines into fully detailed
proofs. In order to validate this approach to proof outlines, we have built the
ACheck system that allows us to take a sequence of theorems and apply the proof
outline "do the obvious induction and close the proof using previously proved
lemmas".
