-
-inductive Track: Context \to Proof \to Sequent \to Prop \def
- | track_proj: \forall P,Q,S,i. Insert S i P Q \to Track Q (lref i) S
- | track_posr: \forall P,h.
- Track P (parx h) (pair (posr h) (posr h))
- | track_impw: \forall P,r,D,a,b. Track P r (pair lleaf D) \to
- Track P (impw r) (pair (impl a b) D)
- | track_impr: \forall P,r. \forall a,b:Formula.
- Track P r (pair a b) \to
- Track P (impr r) (pair lleaf (impl a b))
- | track_impi: \forall P,Q,p,q,r,A,B,D,i. \forall a,b:Formula.
- Track P p (pair A a) \to
- Track P q (pair b B) \to
- Track Q r (pair lleaf D) \to
- Insert (pair A B) i P Q \to
- Track P (impi p q r) (pair (impl a b) D)
+(*
+inductive NTrack: Context \to Proof \to Sequent \to Prop \def
+ | ntrack_proj: \forall P,Q,S,i. Insert S i P Q \to NTrack Q (lref i) S
+ | ntrack_posr: \forall P,h.
+ NTrack P (parx h) (pair (posr h) (posr h))
+ | ntrack_impw: \forall P,r,D,a,b. NTrack P r (pair lleaf D) \to
+ NTrack P (impw r) (pair (impl a b) D)
+ | ntrack_impr: \forall P,r. \forall a,b:Formula.
+ NTrack P r (pair a b) \to
+ NTrack P (impr r) (pair lleaf (impl a b))
+ | ntrack_impi: \forall P,Q,p,q,r,A,B,D,i. \forall a,b:Formula.
+ NTrack P p (pair A a) \to
+ NTrack P q (pair b B) \to
+ NTrack Q r (pair lleaf D) \to
+ Insert (pair A B) i P Q \to
+ NTrack P (impi p q r) (pair (impl a b) D)