X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Faaa_lift.ma;h=f0b5f8a4081ef7a7027979c44c9da6bce0915234;hb=07d915d411ffabeb0c7cd678f00cbeca53ae8276;hp=992c8139cacfff087bae29b81d5ffc7b4d5b257d;hpb=f16bbb93ecb40fa40f736e0b1158e1c7676a640a;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma
index 992c8139c..f0b5f8a40 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma
@@ -17,56 +17,57 @@ include "basic_2/static/aaa.ma".
 
 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
 
-(* Properties concerning basic relocation ***********************************)
+(* Properties on basic relocation *******************************************)
 
-lemma aaa_lift: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. ⇩[d, e] L2 ≡ L1 →
-                ∀T2. ⇧[d, e] T1 ≡ T2 → L2 ⊢ T2 ⁝ A.
-#L1 #T1 #A #H elim H -L1 -T1 -A
-[ #L1 #k #L2 #d #e #_ #T2 #H
+lemma aaa_lift: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀L2,s,d,e. ⇩[s, d, e] L2 ≡ L1 →
+                ∀T2. ⇧[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
+#G #L1 #T1 #A #H elim H -G -L1 -T1 -A
+[ #G #L1 #k #L2 #s #d #e #_ #T2 #H
   >(lift_inv_sort1 … H) -H //
-| #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #d #e #HL21 #T2 #H
+| #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #s #d #e #HL21 #T2 #H
   elim (lift_inv_lref1 … H) -H * #Hid #H destruct
-  [ elim (ldrop_trans_le … HL21 … HLK1 ?) -L1 /2 width=2/ #X #HLK2 #H
-    elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
-    /3 width=8/
-  | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=8/
+  [ elim (ldrop_trans_le … HL21 … HLK1) -L1 /2 width=2 by lt_to_le/ #X #HLK2 #H
+    elim (ldrop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
+    /3 width=9 by aaa_lref/
+  | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1
+    /3 width=9 by aaa_lref, ldrop_inv_gen/
   ]
-| #a #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
+| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #d #e #HL21 #X #H
   elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /4 width=4/
-| #a #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
+  /4 width=5 by aaa_abbr, ldrop_skip/
+| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #d #e #HL21 #X #H
   elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /4 width=4/
-| #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
+  /4 width=5 by aaa_abst, ldrop_skip/
+| #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #d #e #HL21 #X #H
   elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /3 width=4/
-| #L1 #V1 #T1 #A #_ #_ #IH1 #IH2 #L2 #d #e #HL21 #X #H
+  /3 width=5 by aaa_appl/
+| #G #L1 #V1 #T1 #A #_ #_ #IH1 #IH2 #L2 #s #d #e #HL21 #X #H
   elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /3 width=4/
+  /3 width=5 by aaa_cast/
 ]
 qed.
 
-lemma aaa_inv_lift: ∀L2,T2,A. L2 ⊢ T2 ⁝ A → ∀L1,d,e. ⇩[d, e] L2 ≡ L1 →
-                    ∀T1. ⇧[d, e] T1 ≡ T2 → L1 ⊢ T1 ⁝ A.
-#L2 #T2 #A #H elim H -L2 -T2 -A
-[ #L2 #k #L1 #d #e #_ #T1 #H
+lemma aaa_inv_lift: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀L1,s,d,e. ⇩[s, d, e] L2 ≡ L1 →
+                    ∀T1. ⇧[d, e] T1 ≡ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A.
+#G #L2 #T2 #A #H elim H -G -L2 -T2 -A
+[ #G #L2 #k #L1 #s #d #e #_ #T1 #H
   >(lift_inv_sort2 … H) -H //
-| #I #L2 #K2 #V2 #B #i #HLK2 #_ #IHB #L1 #d #e #HL21 #T1 #H
+| #I #G #L2 #K2 #V2 #B #i #HLK2 #_ #IHB #L1 #s #d #e #HL21 #T1 #H
   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
-  [ elim (ldrop_conf_lt … HL21 … HLK2 ?) -L2 // -Hid /3 width=8/
-  | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // -Hid /3 width=8/
+  [ elim (ldrop_conf_lt … HL21 … HLK2) -L2 /3 width=9 by aaa_lref/
+  | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 /3 width=9 by aaa_lref/
   ]
-| #a #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
+| #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #d #e #HL21 #X #H
   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /4 width=4/
-| #a #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
+  /4 width=5 by aaa_abbr, ldrop_skip/
+| #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #d #e #HL21 #X #H
   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /4 width=4/
-| #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
+  /4 width=5 by aaa_abst, ldrop_skip/
+| #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #d #e #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /3 width=4/
-| #L2 #V2 #T2 #A #_ #_ #IH1 #IH2 #L1 #d #e #HL21 #X #H
+  /3 width=5 by aaa_appl/
+| #G #L2 #V2 #T2 #A #_ #_ #IH1 #IH2 #L1 #s #d #e #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /3 width=4/
+  /3 width=5 by aaa_cast/
 ]
 qed-.