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 ***************************)
lemma cnuw_inv_abbr_pos (h) (G) (L):
∀V,T. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
#h #G #L #V #T1 #H
lemma cnuw_inv_abbr_pos (h) (G) (L):
∀V,T. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
#h #G #L #V #T1 #H
lemma cnuw_abbr_neg (h) (G) (L): ∀V,T. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
#h #G #L #V1 #T1 #n #X #H
elim (cpms_inv_abbr_sn_dx … H) -H *
lemma cnuw_abbr_neg (h) (G) (L): ∀V,T. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
#h #G #L #V1 #T1 #n #X #H
elim (cpms_inv_abbr_sn_dx … H) -H *
lemma cnuw_abst (h) (p) (G) (L): ∀W,T. ❪G,L❫ ⊢ ➡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
lemma cnuw_abst (h) (p) (G) (L): ∀W,T. ❪G,L❫ ⊢ ➡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
qed.
lemma cnuw_cpms_trans (h) (n) (G) (L):
∀T1. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T1 →
∀T2. ❪G,L❫ ⊢ T1 ➡*[h,n] T2 → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T2.
#h #n1 #G #L #T1 #HT1 #T2 #HT12 #n2 #T3 #HT23
qed.
lemma cnuw_cpms_trans (h) (n) (G) (L):
∀T1. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T1 →
∀T2. ❪G,L❫ ⊢ T1 ➡*[h,n] T2 → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T2.
#h #n1 #G #L #T1 #HT1 #T2 #HT12 #n2 #T3 #HT23
qed-.
lemma cnuw_dec_ex (h) (G) (L):
∀T1. ∨∨ ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T1
qed-.
lemma cnuw_dec_ex (h) (G) (L):
∀T1. ∨∨ ❪G,L❫ ⊢ ➡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\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)
#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
[ /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
/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
/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
/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 𝐔❨1❩) #X1 #HVX1
@or_intror @(ex2_2_intro … (ⓓ[p]W1.ⓐX1.U1)) [1,2: /2 width=3 by cpms_theta/ ] #H
]
| 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