additions to Basic_2

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / lift_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma
index 91b03c0b9b5a1339cab8c7ecd152e6a9dab4213e..aa0a30f9559f6c246a5943c1b4ab5c7f9b949846 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_vector.ma
@@ -15,14 +15,48 @@
 include "Basic_2/grammar/term_vector.ma".
 include "Basic_2/substitution/lift.ma".
 
-(* RELOCATION ***************************************************************)
+(* BASIC TERM VECTOR RELOCATION *********************************************)
 
 inductive liftv (d,e:nat) : relation (list term) ≝
 | liftv_nil : liftv d e ◊ ◊
 | liftv_cons: ∀T1s,T2s,T1,T2.
-              â\87\91[d, e] T1 ≡ T2 → liftv d e T1s T2s →
+              â\87§[d, e] T1 ≡ T2 → liftv d e T1s T2s →
               liftv d e (T1 :: T1s) (T2 :: T2s)
 .
 
 interpretation "relocation (vector)" 'RLift d e T1s T2s = (liftv d e T1s T2s).
 
+(* Basic inversion lemmas ***************************************************)
+
+fact liftv_inv_nil1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s → T1s = ◊ → T2s = ◊.
+#T1s #T2s #d #e * -T1s -T2s //
+#T1s #T2s #T1 #T2 #_ #_ #H destruct
+qed.
+
+lemma liftv_inv_nil1: ∀T2s,d,e. ⇧[d, e] ◊ ≡ T2s → T2s = ◊.
+/2 width=5/ qed-.
+
+fact liftv_inv_cons1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s →
+                          ∀U1,U1s. T1s = U1 :: U1s →
+                          ∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] U1s ≡ 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 →
+                       ∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] U1s ≡ U2s &
+                                 T2s = U2 :: U2s.
+/2 width=3/ qed-.
+
+(* Basic properties *********************************************************)
+
+lemma liftv_total: ∀d,e. ∀T1s:list term. ∃T2s. ⇧[d, e] T1s ≡ T2s.
+#d #e #T1s elim T1s -T1s
+[ /2 width=2/
+| #T1 #T1s * #T2s #HT12s
+  elim (lift_total T1 d e) /3 width=2/
+]
+qed-.