X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsubstitution%2Flift_vector.ma;h=ea5458ec70d363be111d731a2846ac01f032fd75;hb=5d669f492522b055f76c627eb89da97d0be05c2a;hp=35ecb653533012cf4692f4663a560bab3c1dbe35;hpb=e8998d29ab83e7b6aa495a079193705b2f6743d3;p=helm.git

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 35ecb6535..ea5458ec7 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift_vector.ma
@@ -18,7 +18,7 @@ include "basic_2/substitution/lift.ma".
 (* BASIC TERM VECTOR RELOCATION *********************************************)
 
 inductive liftv (d,e:nat) : relation (list term) ≝
-| liftv_nil : liftv d e ◊ ◊
+| liftv_nil : liftv d e (◊) (◊)
 | liftv_cons: ∀T1s,T2s,T1,T2.
               ⇧[d, e] T1 ≡ T2 → liftv d e T1s T2s →
               liftv d e (T1 @ T1s) (T2 @ T2s)
@@ -31,10 +31,10 @@ interpretation "relocation (vector)" 'RLift d e T1s T2s = (liftv d e T1s T2s).
 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.
+qed-.
 
 lemma liftv_inv_nil1: ∀T2s,d,e. ⇧[d, e] ◊ ≡ T2s → T2s = ◊.
-/2 width=5/ qed-.
+/2 width=5 by liftv_inv_nil1_aux/ qed-.
 
 fact liftv_inv_cons1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s →
                           ∀U1,U1s. T1s = U1 @ U1s →
@@ -42,21 +42,21 @@ fact liftv_inv_cons1_aux: ∀T1s,T2s,d,e. ⇧[d, e] T1s ≡ T2s →
                                     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/
+| #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 →
                        ∃∃U2,U2s. ⇧[d, e] U1 ≡ U2 & ⇧[d, e] 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/
+[ /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 d e) /3 width=2 by liftv_cons, ex_intro/
 ]
 qed-.