(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/LOGIC/Track/defs".
+
(* PROOF TREE TRACKS
*)
-include "datatypes/Proof.ma".
include "Insert/defs.ma".
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_proj: \forall P,Q,p1,p2,S,i.
+ Insert p1 p2 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 P (prin 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_impi: \forall P,r. \forall a,b:Formula.
+ | track_impr: \forall P,r. \forall a,b:Formula.
Track P r (pair a b) \to
- Track P (impi r) (pair lleaf (impl a b))
- | track_impe: \forall P,Q,r,D,i. \forall a,b:Formula.
- Track Q r (pair lleaf D) \to
- Insert (pair a b) i P Q \to
- Track P (impe r) (pair (impl a b) D)
-(*
- | track_impe: \forall P,p,q,r,A,B,D,a,b.
- Track P p (pair A (rinj a)) \to
- Track P q (pair (linj b) B) \to
- Track (abst P (pair A B)) r (pair lleaf D) \to
- Track P (impe p q r) (pair (linj (impl a b)) D)
-*)
+ Track P (impr r) (pair lleaf (impl a b))
+ | track_impi: \forall P,p,q,r,A,B,D. \forall a,b:Formula.
+ Track P p (pair A a) \to
+ Track P q (pair b B) \to
+ Track (abst P p q (pair A B)) r (pair lleaf D) \to
+ Track P (impi p q r) (pair (impl a b) D)
+ | track_scut: \forall P,p,q,A,B. \forall c:Formula.
+ Track P p (pair A c) \to
+ Track P q (pair c B) \to
+ Track P (scut p q) (pair A B)
.