- degree-based equivalene for terms

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lfpr_lfpr.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lfpr_lfpr.etc
new file mode 100644 (file)
index 0000000..7031e79
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lfpr_lfpr.etc
@@ -0,0 +1,39 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_ltpss_sn.ma".
+include "basic_2/reducibility/ltpr_ltpr.ma".
+include "basic_2/reducibility/lfpr.ma".
+
+(* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
+
+(* Main properties **********************************************************)
+
+theorem lfpr_conf: ∀L0,L1,L2. ⦃L0⦄ ➡ ⦃L1⦄ → ⦃L0⦄ ➡ ⦃L2⦄ →
+                   ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.
+#K0 #L1 #L2 * #K1 #HK01 #HKL1 * #K2 #HK02 #HKL2
+lapply (ltpr_fwd_length … HK01) #H
+>(ltpr_fwd_length … HK02) in H; #H
+elim (ltpr_conf … HK01 … HK02) -K0 #K #HK1 #HK2
+lapply (ltpss_sn_fwd_length … HKL1) #H1
+lapply (ltpss_sn_fwd_length … HKL2) #H2
+>H1 in HKL1 H; -H1 #HKL1
+>H2 in HKL2; -H2 #HKL2 #H
+elim (ltpr_ltpss_sn_conf … HKL1 … HK1) -K1 #K1 #HK1 #HLK1
+elim (ltpr_ltpss_sn_conf … HKL2 … HK2) -K2 #K2 #HK2 #HLK2
+elim (ltpss_sn_conf … HK1 … HK2) -K #K #HK1 #HK2
+lapply (ltpr_fwd_length … HLK1) #H1
+lapply (ltpr_fwd_length … HLK2) #H2
+/3 width=5/
+qed.