1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/relocation/fsup.ma".
16 include "basic_2/relocation/ldrop_lpx_sn.ma".
17 include "basic_2/reduction/cpr_lift.ma".
18 include "basic_2/reduction/lpr.ma".
20 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
22 (* Properies on local environment slicing ***********************************)
24 (* Basic_1: includes: wcpr0_drop *)
25 lemma lpr_ldrop_conf: ∀G. dropable_sn (lpr G).
26 /3 width=5 by lpx_sn_deliftable_dropable, cpr_inv_lift1/ qed-.
28 (* Basic_1: includes: wcpr0_drop_back *)
29 lemma ldrop_lpr_trans: ∀G. dedropable_sn (lpr G).
30 /3 width=9 by lpx_sn_liftable_dedropable, cpr_lift/ qed-.
32 lemma lpr_ldrop_trans_O1: ∀G. dropable_dx (lpr G).
33 /2 width=3 by lpx_sn_dropable/ qed-.
35 (* Properties on context-sensitive parallel reduction for terms *************)
37 lemma fsup_cpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
38 ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
39 ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃ ⦃G2, L2, U2⦄.
40 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
41 [ #G #L #K #U #T #d #e #HLK #HUT #He #U2 #HU2
42 elim (lift_total U2 d e) #T2 #HUT2
43 lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9/
44 | #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
45 elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HT2
46 elim (lift_total T d e) #U #HTU
47 elim (ldrop_lpr_trans … HLK1 … HK1) -HLK1 -HK1 #L2 #HL12 #HL2K
48 lapply (cpr_lift … HT1 … HL2K … HTU1 … HTU) -HT1 -HTU1 /3 width=11/