(* 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_tneqw h G L V T1) #T2 #HT12 #HnT12
/3 width=2 by/
(* 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 teqw_abbr_neg/
]
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 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, 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« ⊢ T1 ➡*[h,n] T2 & (T1 ≃ 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© ⊢ T1 ➡*[h,n] T2 & (T1 ≃ T2 → ⊥).
#h #G #L #T1 elim T1 -T1 *
[ #s /3 width=5 by cnuw_sort, or_introl/
| #i elim (drops_F_uni L i)
]
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/