milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / lpc / lfpcs_fpcs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/lpc/lfpcs_fpcs.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/lpc/lfpcs_fpcs.etc
new file mode 100644 (file)
index 0000000..8f36888
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/lpc/lfpcs_fpcs.etc
@@ -0,0 +1,52 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/computation/fprs_cprs.ma".
+include "basic_2/computation/lfprs_fprs.ma".
+include "basic_2/equivalence/fpcs_fpcs.ma".
+include "basic_2/equivalence/lfpcs_lfpcs.ma".
+
+(* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
+
+(* Inversion lemmas on context-free parallel equivalence for closures *******)
+
+lemma lfpcs_inv_fpcs: ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ → ∀T. ⦃L1, T⦄ ⬌* ⦃L2, T⦄.
+#L1 #L2 #HL12 #T
+elim (lfpcs_inv_lfprs … HL12) -HL12 #L #HL1 #HL2
+lapply (lfprs_inv_fprs … HL1 T) -HL1
+lapply (lfprs_inv_fprs … HL2 T) -HL2 /2 width=4/
+qed-.
+
+(* Properties on context-free parallel equivalence for closures *************)
+
+lemma fpcs_lfpcs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+#L1 #L2 #T1 #T2 #HT12
+elim (fpcs_inv_fprs … HT12) -HT12 /3 width=5 by fprs_lfprs, lfprs_div/ (**) (* auto too slow without trace *)
+qed.
+
+lemma fpcs_lift: ∀K1,K2,T1,T2. ⦃K1, T1⦄ ⬌* ⦃K2, T2⦄ →
+                 ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ →
+                 ∀d,e. ⇩[d, e] L1 ≡ K1 → ⇩[d, e] L2 ≡ K2 →
+                 ∀U1,U2. ⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 →
+                 ⦃L1, U1⦄ ⬌* ⦃L2, U2⦄.
+#K1 #K2 #T1 #T2 #HT12 #L1 #L2 #HL12 #d #e #HLK1 #HLK2 #U1 #U2 #HTU1 #HTU2
+elim (fpcs_inv_fprs … HT12) -HT12 #K #T #HT1 #HT2
+elim (lift_total T d e) #U #HTU
+elim (fprs_lift … HT1 … HLK1 … HTU1 HTU) -K1 -T1 #K1 #HU1 #_
+elim (fprs_lift … HT2 … HLK2 … HTU2 HTU) -K2 -T2 -T #K2 #HU2 #_ -K -d -e
+lapply (lfpcs_lfprs_conf K1 … HL12) -HL12 /2 width=3/ #H
+lapply (lfpcs_lfprs_strap1 … H K2 ?) -H /2 width=3/ #HK12
+lapply (lfpcs_inv_fpcs … HK12 U) -HK12 #HU
+/3 width=4 by fpcs_fprs_strap2, fpcs_fprs_div/
+qed.