- revision of ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / lift_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift_vector.ma
index 35ecb653533012cf4692f4663a560bab3c1dbe35..6876229e4cc79b9265d44e54214cfc0c88435907 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift_vector.ma
@@ -17,46 +17,46 @@ include "basic_2/substitution/lift.ma".
 
 (* BASIC TERM VECTOR RELOCATION *********************************************)
 
-inductive liftv (d,e:nat) : relation (list term) ≝
-| liftv_nil : liftv d e ◊ ◊
+inductive liftv (l) (m): relation (list term) ≝
+| liftv_nil : liftv l m (◊) (◊)
 | liftv_cons: ∀T1s,T2s,T1,T2.
-              â\87§[d, e] T1 â\89¡ T2 â\86\92 liftv d e T1s T2s →
-              liftv d e (T1 @ T1s) (T2 @ T2s)
+              â¬\86[l, m] T1 â\89¡ T2 â\86\92 liftv l m T1s T2s →
+              liftv l m (T1 @ T1s) (T2 @ T2s)
 .
 
-interpretation "relocation (vector)" 'RLift d e T1s T2s = (liftv d e T1s T2s).
+interpretation "relocation (vector)" 'RLift l m T1s T2s = (liftv l m 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 //
+fact liftv_inv_nil1_aux: ∀T1s,T2s,l,m. ⬆[l, m] T1s ≡ T2s → T1s = ◊ → T2s = ◊.
+#T1s #T2s #l #m * -T1s -T2s //
 #T1s #T2s #T1 #T2 #_ #_ #H destruct
-qed.
+qed-.
 
-lemma liftv_inv_nil1: ∀T2s,d,e. ⇧[d, e] ◊ ≡ T2s → T2s = ◊.
-/2 width=5/ qed-.
+lemma liftv_inv_nil1: ∀T2s,l,m. ⬆[l, m] ◊ ≡ T2s → T2s = ◊.
+/2 width=5 by liftv_inv_nil1_aux/ qed-.
 
-fact liftv_inv_cons1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s →
+fact liftv_inv_cons1_aux: ∀T1s,T2s,l,m. ⬆[l, m] 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[l, m] U1 â\89¡ U2 & â¬\86[l, m] U1s ≡ U2s &
                                     T2s = U2 @ U2s.
-#T1s #T2s #d #e * -T1s -T2s
+#T1s #T2s #l #m * -T1s -T2s
 [ #U1 #U1s #H destruct
-| #T1s #T2s #T1 #T2 #HT12 #HT12s #U1 #U1s #H destruct /2 width=5/
+| #T1s #T2s #T1 #T2 #HT12 #HT12s #U1 #U1s #H destruct /2 width=5 by ex3_2_intro/
 ]
-qed.
+qed-.
 
-lemma liftv_inv_cons1: ∀U1,U1s,T2s,d,e. ⇧[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: ∀U1,U1s,T2s,l,m. ⬆[l, m] U1 @ U1s ≡ T2s →
+                       â\88\83â\88\83U2,U2s. â¬\86[l, m] U1 â\89¡ U2 & â¬\86[l, m] U1s ≡ U2s &
                                  T2s = U2 @ U2s.
-/2 width=3/ qed-.
+/2 width=3 by liftv_inv_cons1_aux/ 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/
+lemma liftv_total: ∀l,m. ∀T1s:list term. ∃T2s. ⬆[l, m] T1s ≡ T2s.
+#l #m #T1s elim T1s -T1s
+[ /2 width=2 by liftv_nil, ex_intro/
 | #T1 #T1s * #T2s #HT12s
-  elim (lift_total T1 d e) /3 width=2/
+  elim (lift_total T1 l m) /3 width=2 by liftv_cons, ex_intro/
 ]
 qed-.