matita/matita/contribs/lambdadelta/basic_2A/etc/lsubr/lpqs_cpqs.etc

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/grammar/lpx_sn_lpx_sn.ma".
  16 include "basic_2/substitution/fsupp.ma".
  17 include "basic_2/unfold/lpqs_ldrop.ma".
  18
  19 (* SN RESTRICTED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ****************)
  20
  21 (* Main properties on context-sensitive rest parallel computation for terms *)
  22
  23 theorem cpqs_trans_lpqs: lpx_sn_transitive cpqs cpqs.
  24 #L0 #T0 @(fsupp_wf_ind … L0 T0) -L0 -T0 #L0 #T0 #IH #L1 * [|*]
  25 [ #I #HL #HT #T #H1 #L2 #HL12 #T2 #HT2 destruct
  26   elim (cpqs_inv_atom1 … H1) -H1
  27   [ #H destruct
  28     elim (cpqs_inv_atom1 … HT2) -HT2
  29     [ #H destruct //
  30     | * #K2 #V #V2 #i #HLK2 #HV2 #HVT2 #H destruct
  31       elim (lpqs_ldrop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
  32       elim (lpqs_inv_pair2 … H) -H #K1 #V1 #HK12 #HV1 #H destruct
  33       lapply (fsupp_lref … HLK1) /3 width=9/
  34     ]
  35   | * #K1 #V1 #V #i #HLK1 #HV1 #HVT #H destruct
  36     elim (lpqs_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
  37     elim (lpqs_inv_pair1 … H) -H #K2 #W2 #HK12 #_ #H destruct
  38     lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
  39     elim (cpqs_inv_lift1 … HT2 … HLK2 … HVT) -L2 -T
  40     lapply (fsupp_lref … HLK1) /3 width=9/
  41   ]
  42 | #a #I #V1 #T1 #HL #HT #X1 #H1 #L2 #HL12 #X2 #H2
  43   elim (cpqs_inv_bind1 … H1) -H1 *
  44   [ #V #T #HV1 #HT1 #H destruct
  45     elim (cpqs_inv_bind1 … H2) -H2 *
  46     [ #V2 #T2 #HV2 #HT2 #H destruct /4 width=5/
  47     | #T2 #HT2 #HXT2 #H1 #H2 destruct /4 width=5/
  48     ]
  49   | #Y1 #HTY1 #HXY1 #H11 #H12 destruct
  50     elim (lift_total X2 0 1) #Y2 #HXY2
  51     lapply (cpqs_lift … H2 (L2.ⓓV1) … HXY1 … HXY2) /2 width=1/ -X1 /4 width=5/
  52   ]
  53 | #I #V1 #T1 #HL #HT #X1 #H1 #L2 #HL12 #X2 #H2
  54   elim (cpqs_inv_flat1 … H1) -H1 *
  55   [ #V #T #HV1 #HT1 #H destruct
  56     elim (cpqs_inv_flat1 … H2) -H2 *
  57     [ #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
  58     | #HX2 #H destruct /3 width=5/
  59     ]
  60   | #HX1 #H destruct /3 width=5/
  61 ]
  62 qed-.
  63
  64 theorem cpqs_trans: ∀L. Transitive … (cpqs L).
  65 /2 width=5 by cpqs_trans_lpqs/ qed-.
  66
  67 (* Properties on context-sensitive rest. parallel computation for terms *****)
  68
  69 lemma lpqs_cpqs_trans: ∀L1,L2. L1 ⊢ ➤* L2 →
  70                        ∀T1,T2. L2 ⊢ T1 ➤* T2 → L1 ⊢ T1 ➤* T2.
  71 /2 width=5 by cpqs_trans_lpqs/ qed-.