inductive liftsv (des:list2 nat nat) : relation (list term) ≝
| liftsv_nil : liftsv des (◊) (◊)
| liftsv_cons: ∀T1s,T2s,T1,T2.
- â\87§*[des] T1 ≡ T2 → liftsv des T1s T2s →
+ â¬\86*[des] T1 ≡ T2 → liftsv des T1s T2s →
liftsv des (T1 @ T1s) (T2 @ T2s)
.
(* Basic inversion lemmas ***************************************************)
(* Basic_1: was: lifts1_flat (left to right) *)
-lemma lifts_inv_applv1: â\88\80V1s,U1,T2,des. â\87§*[des] Ⓐ V1s. U1 ≡ T2 →
- â\88\83â\88\83V2s,U2. â\87§*[des] V1s â\89¡ V2s & â\87§*[des] U1 ≡ U2 &
+lemma lifts_inv_applv1: â\88\80V1s,U1,T2,des. â¬\86*[des] Ⓐ V1s. U1 ≡ T2 →
+ â\88\83â\88\83V2s,U2. â¬\86*[des] V1s â\89¡ V2s & â¬\86*[des] U1 ≡ U2 &
T2 = Ⓐ V2s. U2.
#V1s elim V1s -V1s normalize
[ #T1 #T2 #des #HT12
(* Basic properties *********************************************************)
(* Basic_1: was: lifts1_flat (right to left) *)
-lemma lifts_applv: â\88\80V1s,V2s,des. â\87§*[des] V1s ≡ V2s →
- â\88\80T1,T2. â\87§*[des] T1 ≡ T2 →
- â\87§*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
+lemma lifts_applv: â\88\80V1s,V2s,des. â¬\86*[des] V1s ≡ V2s →
+ â\88\80T1,T2. â¬\86*[des] T1 ≡ T2 →
+ â¬\86*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
#V1s #V2s #des #H elim H -V1s -V2s /3 width=1 by lifts_flat/
qed.