(**************************************************************************)
include "basic_2/notation/relations/preditnormal_4.ma".
-include "static_2/syntax/tweq.ma".
+include "static_2/syntax/teqw.ma".
include "basic_2/rt_computation/cpms.ma".
(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
definition cnuw (h) (G) (L): predicate term ≝
- λT1. â\88\80n,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n] T2 â\86\92 T1 â\89\85 T2.
+ λT1. â\88\80n,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n] T2 â\86\92 T1 â\89\83 T2.
interpretation
"normality for t-unbound weak head context-sensitive parallel rt-transition (term)"
[ lapply (H 0 W ?) [ /3 width=3 by cpm_cpms, cpm_delta/ ]
| lapply (H 1 W ?) [ /3 width=3 by cpm_cpms, cpm_ell/ ]
] -H #HW
-lapply (tweq_inv_lref_sn … HW) -HW #H destruct
+lapply (teqw_inv_lref_sn … HW) -HW #H destruct
/2 width=5 by lifts_inv_lref2_uni_lt/
qed-.
∀V,T. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] ⓝV.T → ⊥.
#h #G #L #V #T #H
lapply (H 0 T ?) [ /3 width=1 by cpm_cpms, cpm_eps/ ] -H #H
-/2 width=3 by tweq_inv_cast_xy_y/
+/2 width=3 by teqw_inv_cast_xy_y/
qed-.
(* Basic forward lemmas *****************************************************)
∀V,T. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] ⓐV.T → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T.
#h #G #L #V #T1 #HT1 #n #T2 #HT12
lapply (HT1 n (ⓐV.T2) ?) -HT1
-/2 width=3 by cpms_appl_dx, tweq_inv_appl_bi/
+/2 width=3 by cpms_appl_dx, teqw_inv_appl_bi/
qed-.