+++ /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/cpr_ltpss_dx.ma".
-include "basic_2/computation/cprs_tpss.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
-
-(* Properties concerning dx partial unfold on local environments ************)
-
-lemma cprs_ltpss_dx_conf: ∀L1,T,U1. L1 ⊢ T ➡* U1 →
- ∀L2,d,e. L1 ▶* [d, e] L2 →
- ∃∃U2. L2 ⊢ T ➡* U2 & L2 ⊢ U1 ▶* [d, e] U2.
-#L1 #T #U1 #H @(cprs_ind … H) -U1 /2 width=3/
-#T1 #U1 #_ #HTU1 #IHT1 #L2 #d #e #HL12
-elim (IHT1 … HL12) -IHT1 #U #HTU #HT1U
-elim (ltpss_dx_cpr_conf … HTU1 … HL12) -L1 #U0 #HT1U0 #HU10
-elim (cpr_tpss_conf … HT1U0 … HT1U) -T1 #U2 #HU02 #HU2
-lapply (tpss_trans_eq … HU10 HU02) -U0 /3 width=3/
-qed-.
-
-lemma cprs_ltpss_dx_tpss_conf: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 →
- ∀L2,d,e. L1 ▶* [d, e] L2 →
- ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
- ∃∃U2. L2 ⊢ T2 ➡* U2 & L2 ⊢ U1 ▶* [d, e] U2.
-#L1 #T1 #U1 #HTU1 #L2 #d #e #HL12 #T2 #HT12
-elim (cprs_ltpss_dx_conf … HTU1 … HL12) -L1 #U #HT1U #HU1
-elim (cprs_tpss_conf … HT1U … HT12) -T1 #T #HUT #HT2
-lapply (tpss_trans_eq … HU1 HUT) -U /2 width=3/
-qed-.
-
-lemma cprs_ltpss_dx_tpss2_conf: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 →
- ∀L2,d,e. L1 ▶* [d, e] L2 →
- ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
- ∀U2. L2 ⊢ U1 ▶* [d, e] U2 →
- ∃∃U. L2 ⊢ T2 ➡* U & L2 ⊢ U2 ▶* [d, e] U.
-#L1 #T1 #U1 #HTU1 #L2 #d #e #HL12 #T2 #HT12 #U2 #HU12
-elim (cprs_ltpss_dx_tpss_conf … HTU1 … HL12 … HT12) -L1 -T1 #U #HT2U #HU1
-elim (tpss_conf_eq … HU12 … HU1) -U1 #U0 #HU20 #HU0
-lapply (cprs_tpss_trans … HT2U … HU0) -U /2 width=3/
-qed-.