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/fquq_alt.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 fqu_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
41 /3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/
42 #G #L #K #U #T #e #HLK #HUT #U2 #HU2
43 elim (lift_total U2 0 (e+1)) #T2 #HUT2
44 lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/
47 lemma fquq_cpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
48 ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
49 ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
50 #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H
51 [ #HT12 elim (fqu_cpr_trans … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
52 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/