inductive liftv (d,e:nat) : relation (list term) ≝
| liftv_nil : liftv d e (◊) (◊)
| liftv_cons: ∀T1s,T2s,T1,T2.
- â\87§[d, e] T1 ≡ T2 → liftv d e T1s T2s →
+ â¬\86[d, e] T1 ≡ T2 → liftv d e T1s T2s →
liftv d e (T1 @ T1s) (T2 @ T2s)
.
(* Basic inversion lemmas ***************************************************)
-fact liftv_inv_nil1_aux: â\88\80T1s,T2s,d,e. â\87§[d, e] T1s ≡ T2s → T1s = ◊ → T2s = ◊.
+fact liftv_inv_nil1_aux: â\88\80T1s,T2s,d,e. â¬\86[d, e] T1s ≡ T2s → T1s = ◊ → T2s = ◊.
#T1s #T2s #d #e * -T1s -T2s //
#T1s #T2s #T1 #T2 #_ #_ #H destruct
qed-.
-lemma liftv_inv_nil1: â\88\80T2s,d,e. â\87§[d, e] ◊ ≡ T2s → T2s = ◊.
+lemma liftv_inv_nil1: â\88\80T2s,d,e. â¬\86[d, e] ◊ ≡ T2s → T2s = ◊.
/2 width=5 by liftv_inv_nil1_aux/ qed-.
-fact liftv_inv_cons1_aux: â\88\80T1s,T2s,d,e. â\87§[d, e] T1s ≡ T2s →
+fact liftv_inv_cons1_aux: â\88\80T1s,T2s,d,e. â¬\86[d, e] T1s ≡ T2s →
∀U1,U1s. T1s = U1 @ U1s →
- â\88\83â\88\83U2,U2s. â\87§[d, e] U1 â\89¡ U2 & â\87§[d, e] U1s ≡ U2s &
+ â\88\83â\88\83U2,U2s. â¬\86[d, e] U1 â\89¡ U2 & â¬\86[d, e] U1s ≡ U2s &
T2s = U2 @ U2s.
#T1s #T2s #d #e * -T1s -T2s
[ #U1 #U1s #H destruct
]
qed-.
-lemma liftv_inv_cons1: â\88\80U1,U1s,T2s,d,e. â\87§[d, e] U1 @ U1s ≡ T2s →
- â\88\83â\88\83U2,U2s. â\87§[d, e] U1 â\89¡ U2 & â\87§[d, e] U1s ≡ U2s &
+lemma liftv_inv_cons1: â\88\80U1,U1s,T2s,d,e. â¬\86[d, e] U1 @ U1s ≡ T2s →
+ â\88\83â\88\83U2,U2s. â¬\86[d, e] U1 â\89¡ U2 & â¬\86[d, e] U1s ≡ U2s &
T2s = U2 @ U2s.
/2 width=3 by liftv_inv_cons1_aux/ qed-.
(* Basic properties *********************************************************)
-lemma liftv_total: â\88\80d,e. â\88\80T1s:list term. â\88\83T2s. â\87§[d, e] T1s ≡ T2s.
+lemma liftv_total: â\88\80d,e. â\88\80T1s:list term. â\88\83T2s. â¬\86[d, e] T1s ≡ T2s.
#d #e #T1s elim T1s -T1s
[ /2 width=2 by liftv_nil, ex_intro/
| #T1 #T1s * #T2s #HT12s