- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cpr / cpcs_ltpss_dx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpcs_ltpss_dx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpcs_ltpss_dx.etc
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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/cprs_ltpss_dx.ma".
+include "basic_2/equivalence/cpcs_cpcs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
+
+(* Properties concerning dx partial unfold on local environments ************)
+
+lemma cpcs_ltpss_dx_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
+                          ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
+#L1 #L2 #d #e #HL12 #T1 #T2 #H
+elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
+elim (cprs_ltpss_dx_conf … HT1 … HL12) -HT1 #U1 #HTU1 #H1
+elim (cprs_ltpss_dx_conf … HT2 … HL12) -L1 #U2 #HTU2 #H2
+elim (tpss_conf_eq … H1 … H2) -T #U #HU1 #HU2
+lapply (cprs_tpss_trans … HTU1 … HU1) -U1
+lapply (cprs_tpss_trans … HTU2 … HU2) -U2 /2 width=3/
+qed-.
+
+lemma cpcs_ltpss_dx_tpss_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
+                               ∀T,T2. L1 ⊢ T ⬌* T2 →
+                               ∀T1. L2 ⊢ T ▶* [d, e] T1 →
+                               L2 ⊢ T1 ⬌* T2.
+#L1 #L2 #d #e #HL12 #T #T2 #HT2 #T1 #HT1
+lapply (cpcs_ltpss_dx_conf … HL12 … HT2) -L1 #HT2
+lapply (cpcs_tpss_conf … HT1 … HT2) -T //
+qed-.
+
+lemma cpcs_ltpss_dx_tpss2_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
+                                ∀T1,T2. L1 ⊢ T1 ⬌* T2 →
+                                ∀T3. L2 ⊢ T1 ▶* [d, e] T3 →
+                                ∀T4. L2 ⊢ T2 ▶* [d, e] T4 →
+                                L2 ⊢ T3 ⬌* T4.
+#L1 #L2 #d #e #HL12 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24
+lapply (cpcs_ltpss_dx_tpss_conf … HL12 … HT12 … HT13) -L1 -T1 #HT32
+lapply (cpcs_tpss_strap1 … HT32 … HT24) -T2 //
+qed-.