renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpx_req.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_req.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_req.ma
new file mode 100644 (file)
index 0000000..44dcfb5
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_req.ma
@@ -0,0 +1,63 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/req.ma".
+include "basic_2/rt_transition/rpx_fsle.ma".
+
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+
+(* Properties with syntactic equivalence for lenvs on referred entries ******)
+
+(* Basic_2A1: was: lleq_cpx_trans *)
+lemma req_cpx_trans: ∀h,G. req_transitive (cpx h G).
+#h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2 /2 width=2 by cpx_ess/
+[ #I #G #K2 #V1 #V2 #W2 #_ #IH #HVW2 #L1 #H
+  elim (req_inv_zero_pair_dx … H) -H #K1 #HK12 #H destruct
+  /3 width=3 by cpx_delta/
+| #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
+  elim (req_inv_lref_bind_dx … H) -H #I1 #K1 #HK12 #H destruct
+  /3 width=3 by cpx_lref/
+| #p #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
+  elim (req_inv_bind … H) -H /3 width=1 by cpx_bind/
+| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
+  elim (req_inv_flat … H) -H /3 width=1 by cpx_flat/
+| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IH #L1 #H
+  elim (req_inv_bind … H) -H /3 width=3 by cpx_zeta/
+| #G #L2 #W1 #T1 #T2 #_ #IH #L1 #H
+  elim (req_inv_flat … H) -H /3 width=1 by cpx_eps/
+| #G #L2 #W1 #W2 #T1 #_ #IH #L1 #H
+  elim (req_inv_flat … H) -H /3 width=1 by cpx_ee/
+| #p #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H
+  elim (req_inv_flat … H) -H #HV1 #H
+  elim (req_inv_bind … H) -H /3 width=1 by cpx_beta/
+| #p #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV1 #IHW12 #IHT12 #HV2 #L1 #H
+  elim (req_inv_flat … H) -H #HV1 #H
+  elim (req_inv_bind … H) -H /3 width=3 by cpx_theta/
+]
+qed-.
+(*
+(* Basic_2A1: was: cpx_lleq_conf *)
+lemma cpx_req_conf: ∀h,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h] T2 →
+                    ∀L1. L2 ≘[T1] L1 → ⦃G, L1⦄ ⊢ T1 ⬈[h] T2.
+/3 width=3 by req_cpx_trans, req_sym/ qed-.
+*)
+(* Basic_2A1: was: cpx_lleq_conf_sn *)
+lemma cpx_req_conf_sn: ∀h,G. s_r_confluent1 … (cpx h G) req.
+/2 width=5 by cpx_rex_conf/ qed-.
+(*
+(* Basic_2A1: was: cpx_lleq_conf_dx *)
+lemma cpx_req_conf_dx: ∀h,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h] T2 →
+                       ∀L1. L1 ≘[T1] L2 → L1 ≘[T2] L2.
+/4 width=6 by cpx_req_conf_sn, req_sym/ qed-.
+*)