- strong normalization of abbreviation proved

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / csn_lcpr.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lcpr.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lcpr.ma
new file mode 100644 (file)
index 0000000..88c4927
--- /dev/null
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lcpr.ma
@@ -0,0 +1,45 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_cpr.ma".
+include "Basic_2/computation/cprs_lcpr.ma".
+include "Basic_2/computation/csn_cprs.ma".
+include "Basic_2/computation/csn_lift.ma".
+
+(* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
+
+(* Advanced properties ******************************************************)
+
+lemma csn_lcpr_trans: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T. L1 ⊢ ⬇* T → L2 ⊢ ⬇* T.
+#L1 #L2 #HL12 #T #H @(csn_ind_cprs … H) -T #T #_ #IHT
+@csn_intro #T0 #HLT0 #HT0
+@IHT /2 width=2/ -IHT -HT0 /2 width=3/
+qed.
+
+lemma csn_abbr: ∀L,V. L ⊢ ⬇* V → ∀T. L. ⓓV ⊢ ⬇* T → L ⊢ ⬇* ⓓV. T.
+#L #V #HV @(csn_ind … HV) -V #V #_ #IHV #T #HT @(csn_ind_cprs … HT) -T #T #HT #IHT
+@csn_intro #X #H1 #H2
+elim (cpr_inv_abbr1 … H1) -H1 *
+[ #V0 #V1 #T1 #HLV0 #HLV01 #HLT1 #H destruct
+  lapply (cpr_intro … HLV0 HLV01) -HLV01 #HLV1
+  lapply (ltpr_cpr_trans (L. ⓓV) … HLT1) /2 width=1/ -V0 #HLT1
+  elim (eq_false_inv_tpair … H2) -H2
+  [ #HV1 @IHV // /2 width=1/ -HV1
+    @(csn_lcpr_trans (L. ⓓV)) /2 width=1/ -HLV1 /2 width=3/
+  | -IHV -HLV1 * #H destruct /3 width=1/
+  ]
+| -IHV -IHT -H2 #T0 #HT0 #HLT0
+  lapply (csn_inv_lift … HT … HT0) -HT /2 width=3/
+]
+qed.