(* *)
(**************************************************************************)
-include "static_2/static/reqx_drops.ma".
+include "static_2/static/reqg_drops.ma".
include "basic_2/rt_transition/lpx_drops.ma".
include "basic_2/rt_computation/rsx_length.ma".
include "basic_2/rt_computation/rsx_fqup.ma".
-(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+(* STRONGLY NORMALIZING REFERRED LOCAL ENVS FOR EXTENDED RT-TRANSITION ******)
(* Properties with generic relocation ***************************************)
(* Note: this uses length *)
(* Basic_2A1: uses: lsx_lift_le lsx_lift_ge *)
-lemma rsx_lifts (h) (G):
- d_liftable1_isuni ā¦ (Ī»L,T. G ā¢ ā¬*š[h,T] L).
-#h #G #K #T #H @(rsx_ind ā¦ H) -K
+lemma rsx_lifts (G):
+ d_liftable1_isuni ā¦ (Ī»L,T. G ā¢ ā¬*š[T] L).
+#G #K #T #H @(rsx_ind ā¦ H) -K
#K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rsx_intro
#L2 #HL12 #HnL12 elim (lpx_drops_conf ā¦ HLK1 ā¦ HL12)
-/5 width=9 by reqx_lifts_bi, lpx_fwd_length/
+/5 width=9 by reqg_lifts_bi, lpx_fwd_length/
qed-.
(* Inversion lemmas on relocation *******************************************)
(* Basic_2A1: uses: lsx_inv_lift_le lsx_inv_lift_be lsx_inv_lift_ge *)
-lemma rsx_inv_lifts (h) (G):
- d_deliftable1_isuni ā¦ (Ī»L,T. G ā¢ ā¬*š[h,T] L).
-#h #G #L #U #H @(rsx_ind ā¦ H) -L
+lemma rsx_inv_lifts (G):
+ d_deliftable1_isuni ā¦ (Ī»L,T. G ā¢ ā¬*š[T] L).
+#G #L #U #H @(rsx_ind ā¦ H) -L
#L1 #_ #IH #b #f #K1 #HLK1 #Hf #T #HTU @rsx_intro
#K2 #HK12 #HnK12 elim (drops_lpx_trans ā¦ HLK1 ā¦ HK12) -HK12
-/4 width=10 by reqx_inv_lifts_bi/
+/4 width=10 by reqg_inv_lifts_bi/
qed-.
(* Advanced properties ******************************************************)
(* Basic_2A1: uses: lsx_lref_free *)
-lemma rsx_lref_atom_drops (h) (G):
- āL,i. ā©*[ā»,šāØiā©] L ā ā ā G ā¢ ā¬*š[h,#i] L.
-#h #G #L1 #i #HL1
+lemma rsx_lref_atom_drops (G):
+ āL,i. ā©*[ā»,šāØiā©] L ā ā ā G ā¢ ā¬*š[#i] L.
+#G #L1 #i #HL1
@(rsx_lifts ā¦ (#0) ā¦ HL1) -HL1 //
qed.
(* Basic_2A1: uses: lsx_lref_skip *)
-lemma rsx_lref_unit_drops (h) (G):
- āI,L,K,i. ā©[i] L ā K.ā¤[I] ā G ā¢ ā¬*š[h,#i] L.
-#h #G #I #L1 #K1 #i #HL1
+lemma rsx_lref_unit_drops (G):
+ āI,L,K,i. ā©[i] L ā K.ā¤[I] ā G ā¢ ā¬*š[#i] L.
+#G #I #L1 #K1 #i #HL1
@(rsx_lifts ā¦ (#0) ā¦ HL1) -HL1 //
qed.
(* Advanced forward lemmas **************************************************)
(* Basic_2A1: uses: lsx_fwd_lref_be *)
-lemma rsx_fwd_lref_pair_drops (h) (G):
- āL,i. G ā¢ ā¬*š[h,#i] L ā
- āI,K,V. ā©[i] L ā K.ā[I]V ā G ā¢ ā¬*š[h,V] K.
-#h #G #L #i #HL #I #K #V #HLK
+lemma rsx_fwd_lref_pair_drops (G):
+ āL,i. G ā¢ ā¬*š[#i] L ā
+ āI,K,V. ā©[i] L ā K.ā[I]V ā G ā¢ ā¬*š[V] K.
+#G #L #i #HL #I #K #V #HLK
lapply (rsx_inv_lifts ā¦ HL ā¦ HLK ā¦ (#0) ?) -L
/2 width=2 by rsx_fwd_pair/
qed-.