The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to
provide a conceptual framework for integrating different proof development tools, thus allowing for
external evidence and for postponing, delegating, or factoring-out side conditions. In particular,
LLFP allows for reducing the number of times a proof-irrelevant check is performed. In this paper
we give a shallow, actually definitional, implementation of LLFP in Coq, i.e. we use Coq both as
host framework and oracle for LLFP. This illuminates the principles underpinning the mechanism
of Lock-types and also suggests how to possibly extend Coq with the features of LLFP. The derived
proof editor is then put to use for developing case-studies on an emerging paradigm, both at logical
and implementation level, which we call fast and loose reasoning following Danielsson et alii [6].
This paradigm trades off efficiency for correctness and amounts to postponing, or running in parallel,
tedious or computationally demanding checks, until we are really sure that the intended goal can be
achieved. Typical examples are branch-prediction in CPUs and optimistic concurrency control
