- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / equivalence / cpcs_cprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.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/cprs.ma".
+include "basic_2/equivalence/cpcs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
+
+(* Properties about context sensitive computation on terms ******************)
+
+(* Basic_1: was: pc3_pr3_r *)
+lemma cpcs_cprs_dx: ∀L,T1,T2. L ⊢ T1 ➡* T2 → L ⊢ T1 ⬌* T2.
+#L #T1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /3 width=3/
+qed.
+
+(* Basic_1: was: pc3_pr3_x *)
+lemma cpcs_cprs_sn: ∀L,T1,T2. L ⊢ T2 ➡* T1 → L ⊢ T1 ⬌* T2.
+#L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/
+qed.
+
+lemma cpcs_cprs_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ➡* T2 → L ⊢ T1 ⬌* T2.
+#L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /2 width=3/
+qed.
+
+lemma cpcs_cprs_strap2: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+#L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /width=1/ /2 width=3/
+qed.
+
+lemma cpcs_cprs_div: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T2 ➡* T → L ⊢ T1 ⬌* T2.
+#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /2 width=3/
+qed.
+
+(* Basic_1: was: pc3_pr3_conf *)
+lemma cpcs_cprs_conf: ∀L,T1,T. L ⊢ T ➡* T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+#L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /width=1/ /2 width=3/
+qed.
+
+(* Basic_1: was: pc3_pr3_t *)
+(* Basic_1: note: pc3_pr3_t should be renamed *)
+lemma cprs_div: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T2 ➡* T → L ⊢ T1 ⬌* T2.
+#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=1/ /2 width=3/
+qed.
+
+lemma cprs_cpr_div: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T2 ➡ T → L ⊢ T1 ⬌* T2.
+/3 width=5 by step, cprs_div/ qed-.
+
+lemma cpr_cprs_div: ∀L,T1,T. L ⊢ T1 ➡ T → ∀T2. L ⊢ T2 ➡* T → L ⊢ T1 ⬌* T2.
+/3 width=3 by step, cprs_div/ qed-.