-(**************************************************************************)
-(* ___ *)
-(* ||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/ltpr_tps.ma".
-include "basic_2/reducibility/cpr_ltpss_sn.ma".
-include "basic_2/reducibility/lfpr.ma".
-include "basic_2/computation/cprs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
-
-(* Properties concerning focalized parallel reduction on local environments *)
-
-lemma ltpr_tpss_trans: ∀L1,L2. L1 ➡ L2 → ∀T1,T2,d,e. L2 ⊢ T1 ▶* [d, e] T2 →
- ∃∃T. L1 ⊢ T1 ▶* [d, e] T & L1 ⊢ T ➡* T2.
-#L1 #L2 #HL12 #T1 #T2 #d #e #H @(tpss_ind … H) -T2
-[ /2 width=3/
-| #T #T2 #_ #HT2 * #T0 #HT10 #HT0
- elim (ltpr_tps_trans … HT2 … HL12) -L2 #T3 #HT3 #HT32
- @(ex2_intro … HT10) -T1 (**) (* explicit constructors *)
- @(cprs_strap1 … T3 …) /2 width=1/ -HT32
- @(cprs_strap1 … HT0) -HT0 /3 width=3/
-]
-qed.
-
-(* Basic_1: was just: pr3_pr0_pr2_t *)
-lemma ltpr_cpr_trans: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡* T2.
-#L1 #L2 #HL12 #T1 #T2 * #T #HT1
-<(ltpr_fwd_length … HL12) #HT2
-elim (ltpr_tpss_trans … HL12 … HT2) -L2 /3 width=3/
-qed.
-
-(* Basic_1: was just: pr3_pr2_pr2_t *)
-lemma lfpr_cpr_trans: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡* T2.
-#L1 #L2 * /3 width=7/
-qed.