milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_sn.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_sn.etc
new file mode 100644 (file)
index 0000000..79ffb7c
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_sn.etc
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/unfold/ltpss_sn_alt.ma".
+include "basic_2/reducibility/ltpr_ltpss_dx.ma".
+
+(* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
+
+(* Properties on sn parallel unfold on local environments *******************)
+
+(* Note: this can also be proved like ltpr_ltpss_dx_conf *)
+lemma ltpr_ltpss_sn_conf: ∀L1,K1,d,e. L1 ⊢ ▶* [d, e] K1 → ∀L2. L1 ➡ L2 →
+                          ∃∃K2. L2 ⊢ ▶* [d, e] K2 & K1 ➡ K2.
+#L1 #K1 #d #e #H
+lapply (ltpss_sn_ltpssa … H) -H #H
+@(ltpssa_ind … H) -K1 /2 width=3/
+#K #K1 #_ #HK1 #IHK #L2 #HL12
+elim (IHK … HL12) -L1 #K2 #HLK2 #HK2
+elim (ltpr_ltpss_dx_conf … HK1 … HK2) -K /3 width=3/
+qed.