matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/aaa_ltpss_dx.etc

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   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/unfold/tpss_tpss.ma".
  16 include "basic_2/unfold/ltpss_dx_ldrop.ma".
  17 include "basic_2/static/aaa_lift.ma".
  18
  19 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  20
  21 (* Properties about dx parallel unfold **************************************)
  22
  23 lemma aaa_ltpss_dx_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
  24                               ∀L2,d,e. L1 ▶* [d, e] L2 →
  25                               ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
  26 #L1 #T1 #A #H elim H -L1 -T1 -A
  27 [ #L1 #k #L2 #d #e #_ #T2 #H
  28   >(tpss_inv_sort1 … H) -H //
  29 | #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #L2 #d #e #HL12 #T2 #H
  30   elim (tpss_inv_lref1 … H) -H
  31   [ #H destruct
  32     elim (lt_or_ge i d) #Hdi
  33     [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
  34       elim (ltpss_dx_inv_tpss11 … H ?) -H /2 width=1/ -Hdi #K2 #V2 #HK12 #HV12 #H destruct
  35       /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
  36     | elim (lt_or_ge i (d + e)) #Hide
  37       [ elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
  38         elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K2 #V2 #HK12 #HV12 #H destruct
  39         /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
  40       | -Hdi
  41         lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide
  42         /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
  43       ]
  44     ]
  45   | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2
  46     elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
  47     elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #HK12 #HV12 #H destruct
  48     lapply (ldrop_mono … HL2K0 … HLK2) -HL2K0 #H destruct
  49     lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2
  50     lapply (tpss_trans_eq … HV12 HVW2) -V2 /3 width=7/
  51   ]
  52 | #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  53   elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
  54 | #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  55   elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
  56 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  57   elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
  58 | #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  59   elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
  60 ]
  61 qed.
  62
  63 lemma aaa_ltpss_dx_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
  64                              ∀L2,d,e. L1 ▶* [d, e] L2 →
  65                              ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
  66 /3 width=7/ qed.
  67
  68 lemma aaa_ltpss_dx_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
  69                          ∀L2,d,e. L1 ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
  70 /2 width=7/ qed.
  71
  72 lemma aaa_tpss_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
  73                      ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 → L ⊢ T2 ⁝ A.
  74 /2 width=7/ qed.
  75
  76 lemma aaa_tps_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
  77                     ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 → L ⊢ T2 ⁝ A.
  78 /2 width=7/ qed.