(** 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.