| liftv_nil : liftv d e ◊ ◊
| liftv_cons: ∀T1s,T2s,T1,T2.
⇧[d, e] T1 ≡ T2 → liftv d e T1s T2s →
- liftv d e (T1 :: T1s) (T2 :: T2s)
+ liftv d e (T1 @ T1s) (T2 @ T2s)
.
interpretation "relocation (vector)" 'RLift d e T1s T2s = (liftv d e T1s T2s).
/2 width=5/ qed-.
fact liftv_inv_cons1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s →
- ∀U1,U1s. T1s = U1 :: U1s →
+ ∀U1,U1s. T1s = U1 @ U1s →
∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] U1s ≡ U2s &
- T2s = U2 :: U2s.
+ T2s = U2 @ U2s.
#T1s #T2s #d #e * -T1s -T2s
[ #U1 #U1s #H destruct
| #T1s #T2s #T1 #T2 #HT12 #HT12s #U1 #U1s #H destruct /2 width=5/
]
qed.
-lemma liftv_inv_cons1: ∀U1,U1s,T2s,d,e. ⇧[d, e] U1 :: U1s ≡ T2s →
+lemma liftv_inv_cons1: ∀U1,U1s,T2s,d,e. ⇧[d, e] U1 @ U1s ≡ T2s →
∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] U1s ≡ U2s &
- T2s = U2 :: U2s.
+ T2s = U2 @ U2s.
/2 width=3/ qed-.
(* Basic properties *********************************************************)