(* A minimal preservation property we sometimes require.*)
Definition mem_forward (m1 m2:mem) :=
  (forall b, Mem.valid_block m1 b ->
    Mem.valid_block m2 b /\
    forall ofs p, Mem.perm m2 b ofs Max p -> Mem.perm m1 b ofs Max p).

Lemma compose_meminj_inject_incr: forall j12 j12' j23 j23' (InjIncr12: inject_incr j12 j12') (InjIncr23: inject_incr j23 j23'), inject_incr (compose_meminj j12 j23) (compose_meminj j12' j23').