(* GENERIC TERM VECTOR RELOCATION *******************************************)
inductive liftsv (des:list2 nat nat) : relation (list term) ≝
-| liftsv_nil : liftsv des ◊ ◊
+| liftsv_nil : liftsv des (◊) (◊)
| liftsv_cons: ∀T1s,T2s,T1,T2.
⇧*[des] T1 ≡ T2 → liftsv des T1s T2s →
liftsv des (T1 @ T1s) (T2 @ T2s)
∃∃V2s,U2. ⇧*[des] V1s ≡ V2s & ⇧*[des] U1 ≡ U2 &
T2 = Ⓐ V2s. U2.
#V1s elim V1s -V1s normalize
-[ #T1 #T2 #des #HT12
- @(ex3_2_intro) [3,4: // |1,2: skip | // ] (**) (* explicit constructor *)
+[ #T1 #T2 #des #HT12
+ @ex3_2_intro [3,4: // |1,2: skip | // ] (**) (* explicit constructor *)
| #V1 #V1s #IHV1s #T1 #X #des #H
elim (lifts_inv_flat1 … H) -H #V2 #Y #HV12 #HY #H destruct
elim (IHV1s … HY) -IHV1s -HY #V2s #T2 #HV12s #HT12 #H destruct
- @(ex3_2_intro) [4: // |3: /2 width=2/ |1,2: skip | // ] (**) (* explicit constructor *)
+ @(ex3_2_intro) [4: // |3: /2 width=2 by liftsv_cons/ |1,2: skip | // ] (**) (* explicit constructor *)
]
qed-.
lemma lifts_applv: ∀V1s,V2s,des. ⇧*[des] V1s ≡ V2s →
∀T1,T2. ⇧*[des] T1 ≡ T2 →
⇧*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
-#V1s #V2s #des #H elim H -V1s -V2s // /3 width=1/
+#V1s #V2s #des #H elim H -V1s -V2s /3 width=1 by lifts_flat/
qed.