- more on subject reduction of atomic arity assignment

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / lcprs_aaa.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_aaa.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/reducibility/lcpr_aaa.ma".
+include "basic_2/computation/cprs.ma".
+include "basic_2/computation/lcprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
+
+(* Properties about atomic arity assignment on terms ************************)
+
+lemma aaa_lcprs_conf: ∀L1,T,A. L1 ⊢ T ÷ A → ∀L2. L1 ⊢ ➡* L2 → L2 ⊢ T ÷ A.
+#L1 #T #A #HT #L2 #HL12
+@(TC_Conf3 … (λL,A. L ⊢ T ÷ A) … HT ? HL12) /2 width=3/
+qed.
+
+lemma aaa_cprs_conf: ∀L,T1,A. L ⊢ T1 ÷ A → ∀T2. L ⊢ T1 ➡* T2 → L ⊢ T2 ÷ A.
+#L #T1 #A #HT1 #T2 #HT12
+@(TC_Conf3 … HT1 ? HT12) /2 width=3/
+qed.
+
+lemma aaa_lcprs_cprs_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2. L1 ⊢ ➡* L2 →
+                           ∀T2. L2 ⊢ T1 ➡* T2 → L2 ⊢ T2 ÷ A.
+/3 width=3/ qed.