(** * Memory extensions *)
(**  A store [m2] extends a store [m1] if [m2] can be obtained from [m1] by increasing the sizes of the memory blocks of [m1] (decreasing the low bounds, increasing the high bounds), and replacing some of the [Vundef] values stored in [m1] by more defined values stored in [m2] at the same locations. *)
Record extends' (m1 m2: mem) : Prop :=
mk_extends {
mext_next: nextblock m1 = nextblock m2;
mext_inj:  mem_inj inject_id m1 m2;
mext_perm_inv: forall b ofs k p,
perm m2 b ofs k p ->
perm m1 b ofs k p \/ ~perm m1 b ofs Max Nonempty
}.
Definition extends := extends'.

Theorem valid_pointer_extends:
forall m1 m2 b ofs,
extends m1 m2 -> valid_pointer m1 b ofs = true -> valid_pointer m2 b ofs = true.