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)
     (*/\ readonly m1 b m2*)).

Lemma forward_unchanged_trans: forall P m1 m2 m3, Mem.unchanged_on P m1 m2 -> Mem.unchanged_on P m2 m3 -> mem_forward m1 m2 -> mem_forward m2 m3 -> mem_forward m1 m3 /\ Mem.unchanged_on P m1 m3.