+++ /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/grammar/lpx_sn_lpx_sn.ma".
-include "basic_2/substitution/fsupp.ma".
-include "basic_2/unfold/lpqs_ldrop.ma".
-
-(* SN RESTRICTED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ****************)
-
-(* Main properties on context-sensitive rest parallel computation for terms *)
-
-theorem cpqs_trans_lpqs: lpx_sn_transitive cpqs cpqs.
-#L0 #T0 @(fsupp_wf_ind … L0 T0) -L0 -T0 #L0 #T0 #IH #L1 * [|*]
-[ #I #HL #HT #T #H1 #L2 #HL12 #T2 #HT2 destruct
- elim (cpqs_inv_atom1 … H1) -H1
- [ #H destruct
- elim (cpqs_inv_atom1 … HT2) -HT2
- [ #H destruct //
- | * #K2 #V #V2 #i #HLK2 #HV2 #HVT2 #H destruct
- elim (lpqs_ldrop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
- elim (lpqs_inv_pair2 … H) -H #K1 #V1 #HK12 #HV1 #H destruct
- lapply (fsupp_lref … HLK1) /3 width=9/
- ]
- | * #K1 #V1 #V #i #HLK1 #HV1 #HVT #H destruct
- elim (lpqs_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
- elim (lpqs_inv_pair1 … H) -H #K2 #W2 #HK12 #_ #H destruct
- lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
- elim (cpqs_inv_lift1 … HT2 … HLK2 … HVT) -L2 -T
- lapply (fsupp_lref … HLK1) /3 width=9/
- ]
-| #a #I #V1 #T1 #HL #HT #X1 #H1 #L2 #HL12 #X2 #H2
- elim (cpqs_inv_bind1 … H1) -H1 *
- [ #V #T #HV1 #HT1 #H destruct
- elim (cpqs_inv_bind1 … H2) -H2 *
- [ #V2 #T2 #HV2 #HT2 #H destruct /4 width=5/
- | #T2 #HT2 #HXT2 #H1 #H2 destruct /4 width=5/
- ]
- | #Y1 #HTY1 #HXY1 #H11 #H12 destruct
- elim (lift_total X2 0 1) #Y2 #HXY2
- lapply (cpqs_lift … H2 (L2.ⓓV1) … HXY1 … HXY2) /2 width=1/ -X1 /4 width=5/
- ]
-| #I #V1 #T1 #HL #HT #X1 #H1 #L2 #HL12 #X2 #H2
- elim (cpqs_inv_flat1 … H1) -H1 *
- [ #V #T #HV1 #HT1 #H destruct
- elim (cpqs_inv_flat1 … H2) -H2 *
- [ #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
- | #HX2 #H destruct /3 width=5/
- ]
- | #HX1 #H destruct /3 width=5/
-]
-qed-.
-
-theorem cpqs_trans: ∀L. Transitive … (cpqs L).
-/2 width=5 by cpqs_trans_lpqs/ qed-.
-
-(* Properties on context-sensitive rest. parallel computation for terms *****)
-
-lemma lpqs_cpqs_trans: ∀L1,L2. L1 ⊢ ➤* L2 →
- ∀T1,T2. L2 ⊢ T1 ➤* T2 → L1 ⊢ T1 ➤* T2.
-/2 width=5 by cpqs_trans_lpqs/ qed-.