(* Preservation of allocations *)

Theorem alloc_left_unmapped_inject:
forall f m1 m2 lo hi m1' b1,
inject f m1 m2 ->
alloc m1 lo hi = (m1', b1) ->
exists f',
inject f' m1' m2
/\ inject_incr f f'
/\ f' b1 = None
/\ (forall b, b <> b1 -> f' b = f b).