  We present a streamlined and (hopefully) accessible proof of the
model-completeness of the weak monadic second order version of a dense linear
order with left-endpoint but no right-endpoint in a particular finite
signature. We also show how this can be used to establish model-completeness of
the lattice of finite unions of closed intervals of a dense linear order, i.e.
the lattice of closed definable subsets in a (densely ordered) o-minimal
structure, in a particularly simple signature (comprising binary functions for
union and intersection together with two constant symbols and four unary
function symbols).
