milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / cpr / ltpr_ltpss_dx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_dx.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_dx.etc
new file mode 100644 (file)
index 0000000..00730b7
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_dx.etc
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/ltpr_tpss.ma".
+
+(* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
+
+(* Properties concerning dx parallel unfold on local environments ***********)
+
+lemma ltpr_ltpss_dx_conf: ∀L1,K1,d,e. L1 ▶* [d, e] K1 → ∀L2. L1 ➡ L2 →
+                          ∃∃K2. L2 ▶* [d, e] K2 & K1 ➡ K2.
+#L1 #K1 #d #e #H elim H -L1 -K1 -d -e
+[ /2 width=3/
+| #L1 #I #V1 #X #H
+  elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct /3 width=5/
+| #L1 #K1 #I #V1 #W1 #e #_ #HVW1 #IHLK1 #X #H
+  elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
+  elim (IHLK1 … HL12) -L1 #K2 #HLK2 #HK12
+  elim (ltpr_tpr_tpss_conf … HK12 … HV12 … HVW1) -V1 /3 width=5/
+| #L1 #K1 #I #V1 #W1 #d #e #_ #HVW1 #IHLK1 #X #H
+  elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
+  elim (IHLK1 … HL12) -L1 #K2 #HLK2 #HK12
+  elim (ltpr_tpr_tpss_conf … HK12 … HV12 … HVW1) -V1 /3 width=5/
+]
+qed.