include "basic_2/rt_computation/lprs_cpms.ma".
(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
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):
(* Advanced inversion lemmas ************************************************)
lemma cnuw_inv_abbr_pos (h) (G) (L):
-lemma cnuw_abst (h) (p) (G) (L): â\88\80W,T. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡ð\9d\90\8dð\9d\90\96*[h] â\93\9b{p}W.T.
+lemma cnuw_abst (h) (p) (G) (L): â\88\80W,T. â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8dð\9d\90\96*[h] â\93\9b[p]W.T.
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] T1 →
- â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] T2.
+ 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\88¨â\88¨ â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] T1
- | â\88\83â\88\83n,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 & (T1 â\89\85 T2 → ⊥).
+ 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\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=7 by cnuw_atom_drops, or_introl/
| * * [ #I | * #V ] #K #HLK
[ /3 width=8 by cnuw_unit_drops, or_introl/
#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=7 by cnuw_atom_drops, or_introl/
| * * [ #I | * #V ] #K #HLK
[ /3 width=8 by cnuw_unit_drops, or_introl/
/2 width=5 by lifts_inv_lref2_uni_lt/
]
]
| #l /3 width=5 by cnuw_gref, or_introl/
| #p * [ cases p ] #V1 #T1 #_ #_
/2 width=5 by lifts_inv_lref2_uni_lt/
]
]
| #l /3 width=5 by cnuw_gref, or_introl/
| #p * [ cases p ] #V1 #T1 #_ #_
/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/
/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
[ /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
- | elim (lifts_total V1 ð\9d\90\94â\9d´1â\9dµ) #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
- | @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 (lifts_total V1 ð\9d\90\94â\9d¨1â\9d©) #X1 #HVX1
+ @or_intror @(ex2_2_intro … (ⓓ[p]W1.ⓐX1.U1)) [1,2: /2 width=3 by cpms_theta/ ] #H
+ 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 (teqw_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct