include "basic_2/rt_computation/cnuw_simple.ma".
include "basic_2/rt_computation/cnuw_drops.ma".
-include "basic_2/rt_computation/cprs_tweq.ma".
+include "basic_2/rt_computation/cprs_teqw.ma".
include "basic_2/rt_computation/lprs_cpms.ma".
(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
(* Advanced inversion lemmas ************************************************)
lemma cnuw_inv_abbr_pos (h) (G) (L):
- â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
+ â\88\80V,T. â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
#h #G #L #V #T1 #H
-elim (cprs_abbr_pos_twneq h G L V T1) #T2 #HT12 #HnT12
+elim (cprs_abbr_pos_tneqw h G L V T1) #T2 #HT12 #HnT12
/3 width=2 by/
qed-.
(* Advanced properties ******************************************************)
-lemma cnuw_abbr_neg (h) (G) (L): â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
+lemma cnuw_abbr_neg (h) (G) (L): â\88\80V,T. â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
#h #G #L #V1 #T1 #n #X #H
elim (cpms_inv_abbr_sn_dx … H) -H *
-[ #V2 #T2 #_ #_ #H destruct /1 width=1 by tweq_abbr_neg/
+[ #V2 #T2 #_ #_ #H destruct /1 width=1 by teqw_abbr_neg/
| #X1 #_ #_ #H destruct
]
qed.
-lemma cnuw_abst (h) (p) (G) (L): â\88\80W,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] ⓛ[p]W.T.
+lemma cnuw_abst (h) (p) (G) (L): â\88\80W,T. â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] ⓛ[p]W.T.
#h #p #G #L #W1 #T1 #n #X #H
elim (cpms_inv_abst_sn … H) -H #W2 #T2 #_ #_ #H destruct
-/1 width=1 by tweq_abst/
+/1 width=1 by teqw_abst/
qed.
lemma cnuw_cpms_trans (h) (n) (G) (L):
- â\88\80T1. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T1 →
- â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T2.
+ â\88\80T1. â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] T1 →
+ â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] T2.
#h #n1 #G #L #T1 #HT1 #T2 #HT12 #n2 #T3 #HT23
-/4 width=5 by cpms_trans, tweq_canc_sn/
+/4 width=5 by cpms_trans, teqw_canc_sn/
qed-.
lemma cnuw_dec_ex (h) (G) (L):
- â\88\80T1. â\88¨â\88¨ â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T1
- | â\88\83â\88\83n,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n] T2 & (T1 â\89\85 T2 → ⊥).
+ â\88\80T1. â\88¨â\88¨ â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] T1
+ | â\88\83â\88\83n,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n] T2 & (T1 â\89\83 T2 → ⊥).
#h #G #L #T1 elim T1 -T1 *
[ #s /3 width=5 by cnuw_sort, or_introl/
| #i elim (drops_F_uni L i)
[ /3 width=8 by cnuw_unit_drops, or_introl/
| elim (lifts_total V 𝐔❨↑i❩) #W #HVW
@or_intror @(ex2_2_intro … W) [1,2: /2 width=7 by cpms_delta_drops/ ] #H
- lapply (tweq_inv_lref_sn … H) -H #H destruct
+ lapply (teqw_inv_lref_sn … H) -H #H destruct
/2 width=5 by lifts_inv_lref2_uni_lt/
| elim (lifts_total V 𝐔❨↑i❩) #W #HVW
@or_intror @(ex2_2_intro … W) [1,2: /2 width=7 by cpms_ell_drops/ ] #H
- lapply (tweq_inv_lref_sn … H) -H #H destruct
+ lapply (teqw_inv_lref_sn … H) -H #H destruct
/2 width=5 by lifts_inv_lref2_uni_lt/
]
]
| #l /3 width=5 by cnuw_gref, or_introl/
| #p * [ cases p ] #V1 #T1 #_ #_
- [ elim (cprs_abbr_pos_twneq h G L V1 T1) #T2 #HT12 #HnT12
+ [ elim (cprs_abbr_pos_tneqw h G L V1 T1) #T2 #HT12 #HnT12
/4 width=4 by ex2_2_intro, or_intror/
| /3 width=5 by cnuw_abbr_neg, or_introl/
| /3 width=5 by cnuw_abst, or_introl/
[ /3 width=6 by cnuw_appl_simple, or_introl/
| * #n #T2 #HT12 #HnT12 -HT1
@or_intror @(ex2_2_intro … n (ⓐV1.T2)) [ /2 width=1 by cpms_appl_dx/ ] #H
- lapply (tweq_inv_appl_bi … H) -H /2 width=1 by/
+ lapply (teqw_inv_appl_bi … H) -H /2 width=1 by/
]
| elim (lifts_total V1 𝐔❨1❩) #X1 #HVX1
@or_intror @(ex2_2_intro … (ⓓ[p]W1.ⓐX1.U1)) [1,2: /2 width=3 by cpms_theta/ ] #H
- elim (tweq_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct
+ elim (teqw_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct
| @or_intror @(ex2_2_intro … (ⓓ[p]ⓝW1.V1.U1)) [1,2: /2 width=2 by cpms_beta/ ] #H
- elim (tweq_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct
+ elim (teqw_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct
]
| @or_intror @(ex2_2_intro … T1) [1,2: /2 width=2 by cpms_eps/ ] #H
- /2 width=4 by tweq_inv_cast_xy_y/
+ /2 width=4 by teqw_inv_cast_xy_y/
]
]
qed-.
-lemma cnuw_dec (h) (G) (L): â\88\80T. Decidable (â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T).
+lemma cnuw_dec (h) (G) (L): â\88\80T. Decidable (â\9d¨G,Lâ\9d© ⊢ ➡𝐍𝐖*[h] T).
#h #G #L #T1
elim (cnuw_dec_ex h G L T1)
[ /2 width=1 by or_introl/