(* *)
(**************************************************************************)
-include "static_2/relocation/lifts_tdeq.ma".
+include "static_2/relocation/lifts_teqx.ma".
include "basic_2/rt_transition/cpx_drops_basic.ma".
include "basic_2/rt_transition/cnx.ma".
-(* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
+(* NORMAL TERMS FOR EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION *******)
(* Advanced inversion lemmas ************************************************)
-lemma cnx_inv_abbr_pos (h) (G) (L): ∀V,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃+ⓓV.T⦄ → ⊥.
-#h #G #L #V #U1 #H
-elim (cpx_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
-elim (tdeq_dec U1 U2) #HnU12 [ -HU12 | -HTU2 ]
-[ elim (tdeq_inv_lifts_dx … HnU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
+lemma cnx_inv_abbr_pos (G) (L):
+ ∀V,T. ❨G,L❩ ⊢ ⬈𝐍 +ⓓV.T → ⊥.
+#G #L #V #U1 #H
+elim (cpx_subst G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
+elim (teqx_dec U1 U2) #HnU12 [ -HU12 | -HTU2 ]
+[ elim (teqx_inv_lifts_dx … HnU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
lapply (H T1 ?) -H [ /2 width=3 by cpx_zeta/ ] #H
- /2 width=9 by tdeq_lifts_inv_pair_sn/
+ /2 width=9 by teqx_lifts_inv_pair_sn/
| lapply (H (+ⓓV.U2) ?) -H [ /2 width=1 by cpx_bind/ ] -HU12 #H
- elim (tdeq_inv_pair … H) -H #_ #_ /2 width=1 by/
+ elim (teqx_inv_pair … H) -H #_ #_ /2 width=1 by/
]
qed-.