destruct q.
simpl in *.
apply n.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
+ eapply nd_comp; [ idtac | eapply RCut' ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
apply IHX1.
set (letRecSubproofsToND _ _ _ _ _ branches lrsp) as q.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
+ eapply nd_comp; [ idtac | eapply RCut' ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
apply q.