apply nd_rule.
apply SFlat.
apply (@RLetRec Γ Δ lri x y nil).
- apply (Prelude_error "RLetRec at depth>0").
+ destruct (decide_tree_empty (mapOptionTreeAndFlatten take_arg_types_as_tree y @@@ (h :: t)));
+ [ idtac | apply (Prelude_error "used LetRec on a set of bindings involving a function type") ].
+ destruct (eqd_dec y (mapOptionTree drop_arg_types_as_tree y));
+ [ idtac | apply (Prelude_error "used LetRec on a set of bindings involving a function type") ].
+ rewrite <- e.
+ clear e.
+ eapply nd_comp.
+ eapply nd_rule.
+ eapply SFlat.
+ eapply RArrange.
+ eapply ALeft.
+ eapply AComp.
+ eapply ARight.
+ destruct s.
+ apply (arrangeCancelEmptyTree _ _ e).
+ apply ACanL.
+ eapply nd_comp.
+ eapply nd_rule.
+ eapply SFlat.
+ eapply RArrange.
+ eapply AuAssoc.
+ eapply nd_rule.
+ eapply SFlat.
+ eapply RLetRec.
destruct case_RCase.
simpl.