include "basic_2/rt_computation/lsubsx.ma".
-(* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNCOUNTED RT-TRANSITION ********)
+(* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNBOUND RT-TRANSITION **********)
(* Main properties **********************************************************)
-theorem lsubsx_fix: ∀h,o,f,G,L1,L. G ⊢ L1 ⊆ⓧ[h, o, f] L →
- ∀L2. G ⊢ L ⊆ⓧ[h, o, f] L2 → L = L2.
-#h #o #f #G #L1 #L #H elim H -f -L1 -L
+theorem lsubsx_fix: ∀h,f,G,L1,L. G ⊢ L1 ⊆ⓧ[h,f] L →
+ ∀L2. G ⊢ L ⊆ⓧ[h,f] L2 → L = L2.
+#h #f #G #L1 #L #H elim H -f -L1 -L
[ #f #L2 #H
>(lsubsx_inv_atom_sn … H) -L2 //
| #f #I #K1 #K2 #_ #IH #L2 #H
]
qed-.
-theorem lsubsx_trans: ∀h,o,f,G. Transitive … (lsubsx h o G f).
-#h #o #f #G #L1 #L #H1 #L2 #H2
+theorem lsubsx_trans: ∀h,f,G. Transitive … (lsubsx h G f).
+#h #f #G #L1 #L #H1 #L2 #H2
<(lsubsx_fix … H1 … H2) -L2 //
qed-.