- lfpxs based on tc_lfxs

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lfpxs_lfdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma
new file mode 100644 (file)
index 0000000..9389dd0
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/lfdeq_lfdeq.ma".
+include "basic_2/rt_transition/lfpx_lfdeq.ma".
+include "basic_2/rt_computation/lfpxs_fqup.ma".
+
+(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
+
+(* Properties with degree-based equivalence on referred entries *************)
+
+(* Basic_2A1: was: lleq_lpxs_trans *)
+lemma lfdeq_lfpxs_trans: ∀h,o,G,L2,K2,T. ⦃G, L2⦄ ⊢ ⬈*[h, T] K2 →
+                         ∀L1. L1 ≡[h, o, T] L2 →
+                         ∃∃K1. ⦃G, L1⦄ ⊢ ⬈*[h, T] K1 & K1 ≡[h, o, T] K2.
+#h #o #G #L2 #K2 #T #H @(lfpxs_ind_sn … H) -K2 /2 width=3 by ex2_intro/
+#K #K2 #_ #HK2 #IH #L1 #HT elim (IH … HT) -L2
+#L #HL1 #HT elim (lfdeq_lfpx_trans … HK2 … HT) -K
+/3 width=3 by lfpxs_step_dx, ex2_intro/
+qed-.
+
+(* Basic_2A1: was: lpxs_nlleq_inv_step_sn *)
+lemma lfpxs_lfdneq_inv_step_sn: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → (L1 ≡[h, o, T] L2 → ⊥) →
+                                ∃∃L,L0. ⦃G, L1⦄ ⊢ ⬈[h, T] L & L1 ≡[h, o, T] L → ⊥ & ⦃G, L⦄ ⊢ ⬈*[h, T] L0 & L0 ≡[h, o, T] L2.
+#h #o #G #L1 #L2 #T #H @(lfpxs_ind_dx … H) -L1
+[ #H elim H -H //
+| #L1 #L #H1 #H2 #IH2 #H12 elim (lfdeq_dec h o L1 L T) #H
+  [ -H1 -H2 elim IH2 -IH2 /3 width=3 by lfdeq_trans/ -H12
+    #L0 #L3 #H1 #H2 #H3 #H4 lapply (lfdeq_lfdneq_trans … H … H2) -H2
+    #H2 elim (lfdeq_lfpx_trans … H1 … H) -L
+    #L #H1 #H lapply (lfdneq_lfdeq_div … H … H2) -H2
+    #H2 elim (lfdeq_lfpxs_trans … H3 … H) -L0
+    /3 width=8 by lfdeq_trans, ex4_2_intro/
+  | -H12 -IH2 /3 width=6 by ex4_2_intro/
+  ]
+]
+qed-.