support for abstract candidates of reducibility closed! ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / static / aaa_lift.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/static/aaa_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/static/aaa_lift.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "Basic_2/substitution/ldrop_ldrop.ma".
+include "Basic_2/static/aaa.ma".
+
+(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
+
+(* Properties concerning 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
+  >(lift_inv_sort1 … H) -H //
+| #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #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/
+  ]
+| #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #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
+  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
+  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
+  elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
+  /3 width=4/
+]
+qed.