(**************************************************************************)
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)"
[ #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 *)
[ #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: ∀h,G,L,V,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃ⓝV.T⦄ → ⊥.
#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: ∀h,G,L,s. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃⋆s⦄.
#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: ∀h,p,G,L,W,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃W⦄ → ⦃G,L.ⓛW⦄ ⊢ ⬈[h] 𝐍⦃T⦄ →
⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃ⓛ{p}W.T⦄.
#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.