-(**************************************************************************)
-(* ___ *)
-(* ||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/reducibility/cpr_ltpr.ma".
-include "basic_2/equivalence/cpcs_cpcs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
-
-(* Properties about context-free parallel reduction on local environments ***)
-
-(* Basic_1: was only: pc3_pr0_pr2_t *)
-(* Basic_1: note: pc3_pr0_pr2_t should be renamed *)
-lemma ltpr_cpr_conf: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #HT12
-elim (cpr_ltpr_conf_eq … HT12 … HL12) -L1 #T #HT1 #HT2
-@(cprs_div … T) /2 width=1/ /3 width=1/ (**) (* /4 width=3/ is too long *)
-qed.
-
-(* Basic_1: was: pc3_wcpr0_t *)
-(* Basic_1: note: pc3_wcpr0_t should be renamed *)
-lemma ltpr_cprs_conf: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H @(cprs_ind … H) -T2 //
-#T #T2 #_ #HT2 #IHT1
-@(cpcs_trans … IHT1) -T1 /2 width=3/
-qed.
-
-(* Basic_1: was: pc3_wcpr0 *)
-lemma ltpr_cpcs_conf: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H
-elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
-@(cpcs_canc_dx … T) /2 width=3/
-qed.