Definition val_inject_opt (j: meminj) (v1 v2: option val) :=
  match v1, v2 with Some v1', Some v2' => val_inject j v1' v2'
  | None, None => True
  | _, _ => False
  end.

Lemma inject_separated_incr_fwd: forall j j' m1 m2 j'' m2' (InjSep : inject_separated j j' m1 m2) (InjSep' : inject_separated j' j'' m1 m2') (InjIncr' : inject_incr j' j'') (Fwd: mem_forward m2 m2'), inject_separated j j'' m1 m2.