+++ /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/reducibility/tpr_tpss.ma".
-include "basic_2/reducibility/cpr.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
-
-(* Properties concerning parallel unfold on terms ***************************)
-
-(* Note: we could invoke tpss_weak_all instead of ltpr_fwd_length *)
-(* Basic_1: was only: pr2_subst1 *)
-lemma cpr_tpss_ltpr: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L2 ⊢ T1 ➡ T2 →
- ∀d,e,U1. L1 ⊢ T1 ▶* [d, e] U1 →
- ∃∃U2. L2 ⊢ U1 ➡ U2 & L2 ⊢ T2 ▶* [d, e] U2.
-#L1 #L2 #HL12 #T1 #T2 * #T #HT1 #HT2 #d #e #U1 #HTU1
-elim (tpr_tpss_ltpr … HL12 … HT1 … HTU1) -L1 -HT1 #U #HU1 #HTU
-elim (tpss_conf_eq … HT2 … HTU) -T /3 width=3/
-qed.
-
-lemma cpr_ltpr_conf_eq: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 → ∀L2. L1 ➡ L2 →
- ∃∃T. L2 ⊢ T1 ➡ T & T2 ➡ T.
-#L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12
->(ltpr_fwd_length … HL12) in HT2; #HT2
-elim (tpr_tpss_ltpr … HL12 … HT2) -L1 /3 width=3/
-qed.
-
-lemma cpr_ltpr_conf_tpss: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡ T2 →
- ∀d,e,U1. L1 ⊢ T1 ▶* [d, e] U1 →
- ∃∃U2. L2 ⊢ U1 ➡ U2 & L2 ⊢ T2 ➡ U2.
-#L1 #L2 #HL12 #T1 #T2 #HT12 #d #e #U1 #HTU1
-elim (cpr_ltpr_conf_eq … HT12 … HL12) -HT12 #T #HT1 #HT2
-elim (cpr_tpss_ltpr … HL12 … HT1 … HTU1) -L1 -HT1 #U2 #HU12 #HTU2
-lapply (tpss_weak_all … HTU2) -HTU2 #HTU2 /3 width=5/ (**) (* /4 width=5/ is too slow *)
-qed.