(* *)
(**************************************************************************)
-include "basic_2/rt_computation/jsx.ma".
+include "basic_2/rt_computation/jsx_csx.ma".
-(* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
+(* COMPATIBILITY OF STRONG NORMALIZATION FOR EXTENDED RT-TRANSITION *********)
(* Main properties **********************************************************)
-theorem jsx_fix (h) (G):
- ∀f,L1,L. G ⊢ L1 ⊒[h,f] L → ∀L2. G ⊢ L ⊒[h,f] L2 → L = L2.
-#h #G #f #L1 #L #H elim H -f -L1 -L
-[ #f #L2 #H
+theorem jsx_trans (G): Transitive … (jsx G).
+#G #L1 #L #H elim H -L1 -L
+[ #L2 #H
>(jsx_inv_atom_sn … H) -L2 //
-| #f #I #K1 #K2 #_ #IH #L2 #H
- elim (jsx_inv_push_sn … H) -H /3 width=1 by eq_f2/
-| #f #I #K1 #K2 #_ #IH #L2 #H
- elim (jsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
-| #f #I #K1 #K2 #V #_ #_ #IH #L2 #H
- elim (jsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
+| #I #K1 #K #_ #IH #L2 #H
+ elim (jsx_inv_bind_sn … H) -H *
+ [ #K2 #HK2 #H destruct /3 width=1 by jsx_bind/
+ | #J #K2 #V #HK2 #HV #H1 #H2 destruct /3 width=1 by jsx_pair/
+ ]
+| #I #K1 #K #V #_ #HV #IH #L2 #H
+ elim (jsx_inv_void_sn … H) -H #K2 #HK2 #H destruct
+ /3 width=3 by rsx_jsx_trans, jsx_pair/
]
qed-.
-
-theorem jsx_trans (h) (G): ∀f. Transitive … (jsx h G f).
-#h #G #f #L1 #L #H1 #L2 #H2
-<(jsx_fix … H1 … H2) -L2 //
-qed-.