Ltac exploit_match:=
      unfold match_thread_target,match_thread_source,match_thread_compiled in *;
      match goal with
      | [ H: getThreadC ?i = _ ?c,
             H0: context[match_state2match_thread] |- _ ] =>
        rewrite H in H0; inversion H0; subst; simpl in *; clear H0
      end;
      fold match_thread_target in *;
      fold match_thread_source in *;
      fold match_thread_compiled in *.(* Build the concur_match *)
    Ltac destroy_ev_step_sum:=
      match goal with
      | [ H: ev_step_sum _ _ _ _ _ _ _ |- _ ] => inversion H; clear H
      end.

Lemma strong_tree_leq_xmap: forall {A B} f1 f2 t (leq: option B -> option A -> Prop), (forall a p, leq (Some (f1 p a)) (Some (f2 p a))) -> leq None None -> forall p, bounded_maps.strong_tree_leq (PTree.xmap f1 t p) (@PTree.xmap A A f2 t p) leq.