update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_equivalence / scpes_cpcs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/scpes_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/scpes_cpcs.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/scpds_scpds.ma".
+include "basic_2/equivalence/cpcs_cpcs.ma".
+include "basic_2/equivalence/scpes.ma".
+
+(* STRATIFIED DECOMPOSED PARALLEL EQUIVALENCE FOR TERMS *********************)
+
+(* Inversion lemmas on parallel equivalence for terms ***********************)
+
+lemma scpes_inv_lstas_eq: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
+                          ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, d1] U1 →
+                          ∀U2. ⦃G, L⦄ ⊢ T2 •*[h, d2] U2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
+#h #o #G #L #T1 #T2 #d1 #d2 * #T #HT1 #HT2 #U1 #HTU1 #U2 #HTU2
+/3 width=8 by scpds_inv_lstas_eq, cprs_div/
+qed-.
+
+(* Properties on parallel equivalence for terms *****************************)
+
+lemma cpcs_scpes: ∀h,o,G,L,T1,d11. ⦃G, L⦄ ⊢ T1 ▪[h, o] d11 →
+                  ∀U1,d12. d12 ≤ d11 → ⦃G, L⦄ ⊢ T1 •*[h, d12] U1 →
+                  ∀T2,d21. ⦃G, L⦄ ⊢ T2 ▪[h, o] d21 →
+                  ∀U2,d22. d22 ≤ d21 → ⦃G, L⦄ ⊢ T2 •*[h, d22] U2 →
+                  ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d12, d22] T2.
+#h #o #G #L #T1 #d11 #HT1 #U1 #d12 #Hd121 #HTU1 #T2 #d21 #HT2 #U2 #d22 #Hd221 #HTU2 #HU12
+elim (cpcs_inv_cprs … HU12) -HU12 /3 width=6 by scpds_div, ex4_2_intro/
+qed.