+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T2 #H @(cprs_ind … H) -T2
-/3 width=3 by cpcs_cpr_strap1, cpcs_strap1, cpc_cpcs/
-qed.
-
-(* Basic_1: was: pc3_pr3_x *)
-lemma cpcs_cprs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T2 #H @(cprs_ind_dx … H) -T2
-/3 width=3 by cpcs_cpr_div, cpcs_strap1, cpcs_cprs_dx/
-qed.
-
-lemma cpcs_cprs_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /2 width=3 by cpcs_cpr_strap1/
-qed-.
-
-lemma cpcs_cprs_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /2 width=3 by cpcs_cpr_strap2/
-qed-.
-
-lemma cpcs_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=3 by cpcs_cpr_div/
-qed-.
-
-(* Basic_1: was: pc3_pr3_conf *)
-lemma cpcs_cprs_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /2 width=3 by cpcs_cpr_conf/
-qed-.
-
-(* Basic_1: was: pc3_pr3_t *)
-(* Basic_1: note: pc3_pr3_t should be renamed *)
-lemma cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2
-/2 width=3 by cpcs_cpr_div, cpcs_cprs_dx/
-qed.
-
-lemma cprs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=5 by cpr_cprs, cprs_div/ qed-.
-
-lemma cpr_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=3 by cpr_cprs, cprs_div/ qed-.