- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cpr / cpr_ltpss_sn.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr_ltpss_sn.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr_ltpss_sn.etc
new file mode 100644 (file)
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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/unfold/ltpss_sn_alt.ma".
+include "basic_2/reducibility/cpr.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
+
+(* Properties concerning sn partial unfold on local environments ************)
+
+lemma ltpss_sn_cpr_trans: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                          ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡ T2.
+#L1 #L2 #d #e #HL12 #T1 #T2 *
+lapply (ltpss_sn_weak_full … HL12)
+<(ltpss_sn_fwd_length … HL12) -HL12 /3 width=5/
+qed.
+
+lemma ltpss_sn_cpr_conf: ∀L1,T,U1. L1 ⊢ T ➡ U1 →
+                         ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                         ∃∃U2. L2 ⊢ T ➡ U2 & L1 ⊢ U1 ▶* [d, e] U2.
+#L1 #T #U1 * #U #HTU #HU1 #L2 #d #e #HL12
+lapply (ltpss_sn_fwd_length … HL12) #H >H in HU1; -H #HU1
+elim (ltpss_sn_tpss_conf … HU1 … HL12) -HU1 -HL12 /3 width=3/
+qed-.