update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / teqx / cpxs_teqx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/teqx/cpxs_teqx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/teqx/cpxs_teqx.etc
new file mode 100644 (file)
index 0000000..0de7eb6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/teqx/cpxs_teqx.etc
@@ -0,0 +1,46 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rpx_reqx.ma".
+include "basic_2/rt_computation/cpxs.ma".
+
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
+
+(* Properties with sort-irrelevant equivalence for terms ********************)
+
+lemma teqx_cpxs_trans (G) (L) (T):
+      ∀T1. T1 ≛ T → ∀T2. ❪G,L❫ ⊢ T ⬈* T2 → ❪G,L❫ ⊢ T1 ⬈* T2.
+#G #L #T #T1 #HT1 #T2 #HT2 @(cpxs_ind … HT2) -T2
+[ /3 width=1 by teqx_cpx, cpx_cpxs/
+| /2 width=3 by cpxs_strap1/
+]
+qed-.
+
+(* Note: this requires teqx to be symmetric *)
+(* Nasic_2A1: uses: cpxs_neq_inv_step_sn *)
+lemma cpxs_tneqx_fwd_step_sn (G) (L):
+      ∀T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) →
+      ∃∃T. ❪G,L❫ ⊢ T1 ⬈ T & T1 ≛ T → ⊥ & ❪G,L❫ ⊢ T ⬈* T2.
+#G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
+[ #H elim H -H //
+| #T1 #T0 #HT10 #HT02 #IH #HnT12
+  elim (teqx_dec T1 T0) [ -HT10 -HT02 #HT10 | -IH #HnT10 ]
+  [ elim IH -IH /3 width=3 by teqx_trans/ -HnT12
+    #T #HT0 #HnT0 #HT2
+    lapply (teqx_cpx_trans … HT10 … HT0) -HT0 #HT1
+    /4 width=4 by teqx_canc_sn, ex3_intro/
+  | /3 width=4 by ex3_intro/
+  ]
+]
+qed-.