let rec fsubst W d U on U ≝ match U with
[ TAtom I ⇒ match I with
[ Sort _ ⇒ U
- | LRef i â\87\92 tri â\80¦ i d (#i) (â\86\9f[0, i] W) (#(i-1))
+ | LRef i â\87\92 tri â\80¦ i d (#i) (â\86\91[0, i] W) (#(i-1))
| GRef _ ⇒ U
]
| TPair I V T ⇒ match I with
(* Main properties **********************************************************)
theorem fsubst_delift: ∀K,V,T,L,d.
- â\86\93[0, d] L â\89¡ K. ð\9d\95\93{Abbr} V â\86\92 L â\8a¢ T [d, 1] â\89¡ â\86¡[d ← V] T.
+ â\87\93[0, d] L â\89¡ K. ð\9d\95\93{Abbr} V â\86\92 L â\8a¢ T [d, 1] â\89¡ â\86\93[d ← V] T.
#K #V #T elim T -T
[ * #i #L #d #HLK normalize in ⊢ (? ? ? ? ? %); /2 width=3/
elim (lt_or_eq_or_gt i d) #Hid
(* Main inversion properties ************************************************)
-theorem fsubst_inv_delift: â\88\80K,V,T1,L,T2,d. â\86\93[0, d] L â\89¡ K. ð\9d\95\93{Abbr} V â\86\92
- L â\8a¢ T1 [d, 1] â\89¡ T2 â\86\92 â\86¡[d ← V] T1 = T2.
+theorem fsubst_inv_delift: â\88\80K,V,T1,L,T2,d. â\87\93[0, d] L â\89¡ K. ð\9d\95\93{Abbr} V â\86\92
+ L â\8a¢ T1 [d, 1] â\89¡ T2 â\86\92 â\86\93[d ← V] T1 = T2.
#K #V #T1 elim T1 -T1
[ * #i #L #T2 #d #HLK #H
[ -HLK >(delift_fwd_sort1 … H) -H //
]
]
qed-.
-
\ No newline at end of file