Definition mod_after_alloc (phi: rmap) (lo hi: Z) (b: block) :=
proj1_sig (make_rmap (mod_after_alloc' phi lo hi b) (ghost_of phi)
_
(mod_after_alloc'_ok phi lo hi b) (ghost_of_approx phi)).
Transparent alloc.

Lemma adr_range_zle_fact : forall b lo hi loc,
adr_range (b,lo) (hi-lo) loc ->
zle lo (snd loc) && zlt (snd loc) hi = true.