- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsuba_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma
new file mode 100644 (file)
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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/static/aaa_aaa.ma".
+include "basic_2/static/lsuba_ldrop.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
+
+(* Properties concerning atomic arity assignment ****************************)
+
+lemma lsuba_aaa_conf: ∀L1,V,A. L1 ⊢ V ⁝ A → ∀L2. L1 ⁝⊑ L2 → L2 ⊢ V ⁝ A.
+#L1 #V #A #H elim H -L1 -V -A
+[ //
+| #I #L1 #K1 #V1 #B #i #HLK1 #HV1B #IHV1 #L2 #HL12
+  elim (lsuba_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
+  elim (lsuba_inv_pair1 … H) -H * #K2
+  [ #HK12 #H destruct /3 width=5/
+  | #V2 #A1 #HV1A1 #HV2 #_ #H1 #H2 destruct
+    >(aaa_mono … HV1B … HV1A1) -B -HV1A1 /2 width=5/
+  ]
+| /4 width=2/
+| /4 width=1/
+| /3 width=3/
+| /3 width=1/
+]
+qed.
+
+lemma lsuba_aaa_trans: ∀L2,V,A. L2 ⊢ V ⁝ A → ∀L1. L1 ⁝⊑ L2 → L1 ⊢ V ⁝ A.
+#L2 #V #A #H elim H -L2 -V -A
+[ //
+| #I #L2 #K2 #V2 #B #i #HLK2 #HV2B #IHV2 #L1 #HL12
+  elim (lsuba_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsuba_inv_pair2 … H) -H * #K1
+  [ #HK12 #H destruct /3 width=5/
+  | #V1 #A1 #HV1 #HV2A1 #_ #H1 #H2 destruct
+    >(aaa_mono … HV2B … HV2A1) -B -HV2A1 /2 width=5/
+  ]
+| /4 width=2/
+| /4 width=1/
+| /3 width=3/
+| /3 width=1/
+]
+qed.