matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  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".
  19
  20 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
  21
  22 (* Properies on local environment slicing ***********************************)
  23
  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-.
  27
  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-.
  31
  32 lemma lpr_ldrop_trans_O1: ∀G. dropable_dx (lpr G).
  33 /2 width=3 by lpx_sn_dropable/ qed-.
  34
  35 (* Properties on context-sensitive parallel reduction for terms *************)
  36
  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/
  45 qed-.
  46
  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/
  53 ]
  54 qed-.