+++ /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_lpss.ma".
-include "basic_2/equivalence/cpcs_cpcs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
-
-(* Properties on sn parallel substitution for local environments ************)
-
-lemma cpcs_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
- ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2.
-#L1 #T1 #T2 #H #L2 #HL12
-elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
-elim (cprs_lpss_conf_dx … HT1 … HL12) -HT1 #U1 #H1 #HTU1
-elim (cprs_lpss_conf_dx … HT2 … HL12) -L1 #U2 #H2 #HTU2
-elim (cpss_conf … H1 … H2) -T #U #HU1 #HU2
-lapply (cprs_cpss_trans … HTU1 … HU1) -U1
-lapply (cprs_cpss_trans … HTU2 … HU2) -U2 /2 width=3/
-qed-.
-
-lemma cpcs_cpss_lpss_conf: ∀L1,T,T2. L1 ⊢ T ⬌* T2 → ∀T1. L1 ⊢ T ▶* T1 →
- ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2.
-#L1 #T #T2 #HT2 #T1 #HT1 #L2 #HL12
-lapply (cpcs_lpss_conf … HT2 … HL12) -HT2 #HT2
-elim (lpss_cpss_conf_dx … HT1 … HL12) -L1 #T0 #HT0 #HT10
-lapply (cpcs_cpss_conf … HT0 … HT2) -T #HT02
-lapply (cpcs_cpss_strap2 … HT10 … HT02) -T0 //
-qed-.
-
-lemma cpcs_cpss2_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
- ∀T3. L1 ⊢ T1 ▶* T3 → ∀T4. L1 ⊢ T2 ▶* T4 →
- ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T3 ⬌* T4.
-#L1 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24 #L2 #HL12
-lapply (cpcs_cpss_lpss_conf … HT12 … HT13 … HL12) -T1 #HT32
-elim (lpss_cpss_conf_dx … HT24 … HL12) -L1 #T #HT2 #HT4
-lapply (cpcs_cpss_strap1 … HT32 … HT2) -T2 #HT3
-lapply (cpcs_cpss_div … HT3 … HT4) -T //
-qed-.