(**************************************************************************)
include "basic_2/notation/relations/predtynormal_4.ma".
-include "static_2/syntax/tdeq.ma".
+include "static_2/syntax/teqx.ma".
include "basic_2/rt_transition/cpx.ma".
(* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
definition cnx: ∀h. relation3 genv lenv term ≝
- λh,G,L. NF … (cpx h G L) tdeq.
+ λh,G,L. NF … (cpx h G L) teqx.
interpretation
"normality for unbound context-sensitive parallel rt-transition (term)"
(* Basic inversion lemmas ***************************************************)
-lemma cnx_inv_abst: â\88\80h,p,G,L,V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83â\93\9b{p}V.Tâ¦\84 →
- â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Vâ¦\84 â\88§ â¦\83G,L.â\93\9bVâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Tâ¦\84.
+lemma cnx_inv_abst: â\88\80h,p,G,L,V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªâ\93\9b[p]V.Tâ\9d« →
+ â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªVâ\9d« â\88§ â\9dªG,L.â\93\9bVâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªTâ\9d«.
#h #p #G #L #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (ⓛ{p}V2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
-| #T2 #HT2 lapply (HVT1 (ⓛ{p}V1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2
+[ #V2 #HV2 lapply (HVT1 (ⓛ[p]V2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
+| #T2 #HT2 lapply (HVT1 (ⓛ[p]V1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2
]
-#H elim (tdeq_inv_pair … H) -H //
+#H elim (teqx_inv_pair … H) -H //
qed-.
(* Basic_2A1: was: cnx_inv_abbr *)
-lemma cnx_inv_abbr_neg: â\88\80h,G,L,V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83-â\93\93V.Tâ¦\84 →
- â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Vâ¦\84 â\88§ â¦\83G,L.â\93\93Vâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Tâ¦\84.
+lemma cnx_inv_abbr_neg: â\88\80h,G,L,V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dª-â\93\93V.Tâ\9d« →
+ â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªVâ\9d« â\88§ â\9dªG,L.â\93\93Vâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªTâ\9d«.
#h #G #L #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
+[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
| #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2
]
-#H elim (tdeq_inv_pair … H) -H //
+#H elim (teqx_inv_pair … H) -H //
qed-.
(* Basic_2A1: was: cnx_inv_eps *)
-lemma cnx_inv_cast: â\88\80h,G,L,V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83â\93\9dV.Tâ¦\84 → ⊥.
+lemma cnx_inv_cast: â\88\80h,G,L,V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªâ\93\9dV.Tâ\9d« → ⊥.
#h #G #L #V #T #H lapply (H T ?) -H
-/2 width=6 by cpx_eps, tdeq_inv_pair_xy_y/
+/2 width=6 by cpx_eps, teqx_inv_pair_xy_y/
qed-.
(* Basic properties *********************************************************)
-lemma cnx_sort: â\88\80h,G,L,s. â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83â\8b\86sâ¦\84.
+lemma cnx_sort: â\88\80h,G,L,s. â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªâ\8b\86sâ\9d«.
#h #G #L #s #X #H elim (cpx_inv_sort1 … H) -H
-/2 width=1 by tdeq_sort/
+/2 width=1 by teqx_sort/
qed.
-lemma cnx_abst: â\88\80h,p,G,L,W,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Wâ¦\84 â\86\92 â¦\83G,L.â\93\9bWâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Tâ¦\84 →
- â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83â\93\9b{p}W.Tâ¦\84.
+lemma cnx_abst: â\88\80h,p,G,L,W,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªWâ\9d« â\86\92 â\9dªG,L.â\93\9bWâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªTâ\9d« →
+ â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªâ\93\9b[p]W.Tâ\9d«.
#h #p #G #L #W #T #HW #HT #X #H
elim (cpx_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
-@tdeq_pair [ @HW | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
+@teqx_pair [ @HW | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
qed.