intros ? ? ge mu mu' mu'' incr gsep12 gsep23 b1 b3 d3 map1 map3.
destruct (as_inj mu' b1) as [[b2 d2]|] eqn: map2.
+ eapply gsep12.
- eassumption.
- rewrite (incr b1 b2 d2 map2) in map3; inversion map3. subst; eassumption.
+ eapply gsep23; eauto.
Qed.

Lemma gsep_trans':
forall {F V} (ge:  Genv.t F V) mu mu' mu'',
SM_wd mu'' ->
intern_incr mu' mu'' ->
globals_separate ge mu mu' ->
globals_separate ge mu' mu'' ->
globals_separate ge mu mu''.