(** Injecting a memory into itself. *)
Definition flat_inj (thr: block) : meminj :=
fun (b: block) => if plt b thr then Some(b, 0) else None.
Definition inject_neutral (thr: block) (m: mem) :=
mem_inj (flat_inj thr) m m.
Remark flat_inj_no_overlap:
forall thr m, meminj_no_overlap (flat_inj thr) m.

(* Specifications: *)
Theorem neutral_inject:
forall m, inject_neutral (nextblock m) m -> inject (flat_inj (nextblock m)) m m.
Theorem empty_inject_neutral:
forall thr, inject_neutral thr empty.
Theorem alloc_inject_neutral:
forall thr m lo hi b m',
alloc m lo hi = (m', b) ->
inject_neutral thr m ->
Plt (nextblock m) thr ->
inject_neutral thr m'.
Theorem store_inject_neutral:
forall chunk m b ofs v m' thr,
store chunk m b ofs v = Some m' ->
inject_neutral thr m ->
Plt b thr ->
Val.inject (flat_inj thr) v v ->
inject_neutral thr m'.
Theorem drop_inject_neutral:
forall m b lo hi p m' thr,
drop_perm m b lo hi p = Some m' ->
inject_neutral thr m ->
Plt b thr ->
inject_neutral thr m'.
Theorem neutral_inject:
forall m, inject_neutral (nextblock m) m -> inject (flat_inj (nextblock m)) m m.