induction X; simpl.
- (* the proof from no hypotheses of no conclusions (nd_id0) becomes REmptyGroup *)
- apply nd_rule; apply (org_fc _ _ (REmptyGroup _ _ )). auto.
+ (* the proof from no hypotheses of no conclusions (nd_id0) becomes RVoid *)
+ apply nd_rule; apply (org_fc _ _ (RVoid _ _ )). auto.
(* the proof from hypothesis X of conclusion X (nd_id1) becomes RVar *)
apply nd_rule; apply (org_fc _ _ (RVar _ _ _ _)). auto.
- (* the proof from hypothesis X of no conclusions (nd_weak) becomes RWeak;;REmptyGroup *)
+ (* the proof from hypothesis X of no conclusions (nd_weak) becomes RWeak;;RVoid *)
eapply nd_comp;
[ idtac
| eapply nd_rule
; eapply (org_fc _ _ (RArrange _ _ _ _ _ (RWeak _)))
; auto ].
eapply nd_rule.
- eapply (org_fc _ _ (REmptyGroup _ _)); auto.
+ eapply (org_fc _ _ (RVoid _ _)); auto.
- (* the proof from hypothesis X of two identical conclusions X,,X (nd_copy) becomes RVar;;RBindingGroup;;RCont *)
+ (* the proof from hypothesis X of two identical conclusions X,,X (nd_copy) becomes RVar;;RJoin;;RCont *)
eapply nd_comp; [ idtac | eapply nd_rule; eapply (org_fc _ _ (RArrange _ _ _ _ _ (RCont _))) ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
set (nd_seq_reflexive(SequentCalculus:=@pl_sc _ _ _ _ (SystemFCa _ Γ Δ))
apply q.
apply q.
apply nd_rule.
- eapply (org_fc _ _ (RBindingGroup _ _ _ _ _ _ )).
+ eapply (org_fc _ _ (RJoin _ _ _ _ _ _ )).
auto.
auto.
- (* nd_prod becomes nd_llecnac;;nd_prod;;RBindingGroup *)
+ (* nd_prod becomes nd_llecnac;;nd_prod;;RJoin *)
eapply nd_comp.
apply (nd_llecnac ;; nd_prod IHX1 IHX2).
apply nd_rule.
- eapply (org_fc _ _ (RBindingGroup _ _ _ _ _ _ )).
+ eapply (org_fc _ _ (RJoin _ _ _ _ _ _ )).
auto.
(* nd_comp becomes pl_subst (aka nd_cut) *)
| PCF_RLam Σ tx te => let case_RLam := tt in _
| PCF_RApp Σ tx te p => let case_RApp := tt in _
| PCF_RLet Σ σ₁ σ₂ p => let case_RLet := tt in _
- | PCF_RBindingGroup b c d e => let case_RBindingGroup := tt in _
- | PCF_REmptyGroup => let case_REmptyGroup := tt in _
+ | PCF_RJoin b c d e => let case_RJoin := tt in _
+ | PCF_RVoid => let case_RVoid := tt in _
(*| PCF_RCase T κlen κ θ l x => let case_RCase := tt in _*)
(*| PCF_RLetRec Σ₁ τ₁ τ₂ lev => let case_RLetRec := tt in _*)
end); simpl in *.
(* ga_comp! perhaps this means the ga_curry avoidance can be done by turning lambdas into lets? *)
admit.
- destruct case_REmptyGroup.
+ destruct case_RVoid.
(* ga_id u *)
admit.
- destruct case_RBindingGroup.
+ destruct case_RJoin.
(* ga_first+ga_second; technically this assumes a specific evaluation order, which is bad *)
admit.