update for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma
new file mode 100644 (file)
index 0000000..eb1444b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma
@@ -0,0 +1,49 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rt_transition/cpx_reqx.ma".
+include "basic_2/rt_computation/cpxs_teqx.ma".
+
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Properties with sort-irrelevant equivalence for local environments *******)
+
+(* Basic_2A1: was just: lleq_cpxs_trans *) 
+lemma reqx_cpxs_trans: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
+                       ∀L2. L2 ≛[T0] L0 →
+                       ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
+#h #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
+#T0 #T #HT0 #_ #IH #L2 #HL2
+elim (reqx_cpx_trans … HL2 … HT0) #U1 #H1 #H2
+elim (IH L2) -IH /2 width=5 by cpx_reqx_conf_dx/ -L0 #U2 #H3 #H4
+elim (teqx_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
+/3 width=5 by cpxs_strap2, teqx_trans, ex2_intro/
+qed-.
+
+(* Basic_2A1: was just: cpxs_lleq_conf *) 
+lemma cpxs_reqx_conf: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
+                      ∀L2. L0 ≛[T0] L2 →
+                      ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
+/3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
+
+(* Basic_2A1: was just: cpxs_lleq_conf_dx *) 
+lemma cpxs_reqx_conf_dx: ∀h,G,L2,T1,T2. ⦃G,L2⦄ ⊢ T1 ⬈*[h] T2 →
+                         ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
+#h #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
+qed-.
+
+(* Basic_2A1: was just: lleq_conf_sn *) 
+lemma cpxs_reqx_conf_sn: ∀h,G,L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬈*[h] T2 →
+                         ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
+/4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.