- more properties on strongly normalizing terms

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_cpr.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_cpr.ma
new file mode 100644 (file)
index 0000000..11647e9
--- /dev/null
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_cpr.ma
@@ -0,0 +1,41 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/cpr_cpr.ma".
+include "Basic_2/computation/csn.ma".
+
+(* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
+
+(* Advanced forvard lemmas **************************************************)
+
+fact csn_fwd_pair_sn_aux: ∀L,U. L ⊢ ⬇* U → ∀I,V,T. U = ②{I} V. T → L ⊢ ⬇* V.
+#L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+@csn_intro #V2 #HLV2 #HV2
+@(IH (②{I} V2. T)) -IH // /2 width=1/ -HLV2 #H destruct /2 width=1/
+qed.
+
+(* Basic_1: was: sn3_gen_head *)
+lemma csn_fwd_pair_sn: ∀I,L,V,T. L ⊢ ⬇* ②{I} V. T → L ⊢ ⬇* V.
+/2 width=5/ qed.
+
+fact csn_fwd_bind_dx_aux: ∀L,U. L ⊢ ⬇* U →
+                          ∀I,V,T. U = ⓑ{I} V. T → L. ⓑ{I} V ⊢ ⬇* T.
+#L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+@csn_intro #T2 #HLT2 #HT2
+@(IH (ⓑ{I} V. T2)) -IH // /2 width=1/ -HLT2 #H destruct /2 width=1/
+qed.
+
+(* Basic_1: was: sn3_gen_bind *)
+lemma csn_fwd_bind_dx: ∀I,L,V,T. L ⊢ ⬇* ⓑ{I} V. T → L. ⓑ{I} V ⊢ ⬇* T.
+/2 width=3/ qed.