Definition inflate_initial_mem (w: rmap): rmap :=
    proj1_sig (make_rmap (inflate_initial_mem' w) (ghost_of w) _
            (inflate_initial_mem'_fmap w) (ghost_of_approx w)).

(* Specifications: *)
Lemma inflate_initial_mem_level: forall w, level (inflate_initial_mem w) = level w.
Lemma inflate_initial_mem_all_VALs: forall lev, all_VALs (inflate_initial_mem lev).