- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / lsubr / cpcs_lpss.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/cpcs_lpss.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/cpcs_lpss.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_lpss.ma".
+include "basic_2/equivalence/cpcs_cpcs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
+
+(* Properties on sn parallel substitution for local environments ************)
+
+lemma cpcs_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
+                      ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2.
+#L1 #T1 #T2 #H #L2 #HL12
+elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
+elim (cprs_lpss_conf_dx … HT1 … HL12) -HT1 #U1 #H1 #HTU1
+elim (cprs_lpss_conf_dx … HT2 … HL12) -L1 #U2 #H2 #HTU2
+elim (cpss_conf … H1 … H2) -T #U #HU1 #HU2
+lapply (cprs_cpss_trans … HTU1 … HU1) -U1
+lapply (cprs_cpss_trans … HTU2 … HU2) -U2 /2 width=3/
+qed-.
+
+lemma cpcs_cpss_lpss_conf: ∀L1,T,T2. L1 ⊢ T ⬌* T2 → ∀T1. L1 ⊢ T ▶* T1 →
+                           ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2.
+#L1 #T #T2 #HT2 #T1 #HT1 #L2 #HL12
+lapply (cpcs_lpss_conf … HT2 … HL12) -HT2 #HT2
+elim (lpss_cpss_conf_dx … HT1 … HL12) -L1 #T0 #HT0 #HT10
+lapply (cpcs_cpss_conf … HT0 … HT2) -T #HT02
+lapply (cpcs_cpss_strap2 … HT10 … HT02) -T0 //
+qed-.
+
+lemma cpcs_cpss2_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
+                            ∀T3. L1 ⊢ T1 ▶* T3 → ∀T4. L1 ⊢ T2 ▶* T4 →
+                            ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T3 ⬌* T4.
+#L1 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24 #L2 #HL12
+lapply (cpcs_cpss_lpss_conf … HT12 … HT13 … HL12) -T1 #HT32
+elim (lpss_cpss_conf_dx … HT24 … HL12) -L1 #T #HT2 #HT4
+lapply (cpcs_cpss_strap1 … HT32 … HT2) -T2 #HT3
+lapply (cpcs_cpss_div … HT3 … HT4) -T //
+qed-.