  Loop quantum cosmology in (b, v) variables, which is governed by a unit step
size difference equation, is embedded into a full theory context based on
similar variables. A full theory context here means a theory of quantum gravity
arrived at using the quantisation techniques used in loop quantum gravity,
however based on a different choice of elementary variables and classical gauge
fixing suggested by loop quantum cosmology. From the full theory perspective,
the symmetry reduction is characterised by the vanishing of certain phase space
functions which are implemented as operator equations in the quantum theory.
The loop quantum cosmology dynamics arise as the action of the full theory
Hamiltonian on maximally coarse states in the kernel of the reduction
constraints. An application of this reduction procedure to spherical symmetry
is also sketched, with similar results, but only one canonical pair in (b, v)
form.
