matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma

   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/substitution/ldrop_ldrop.ma".
  16 include "basic_2/static/aaa.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Properties concerning basic relocation ***********************************)
  21
  22 lemma aaa_lift: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. ⇩[d, e] L2 ≡ L1 →
  23                 ∀T2. ⇧[d, e] T1 ≡ T2 → L2 ⊢ T2 ⁝ A.
  24 #L1 #T1 #A #H elim H -L1 -T1 -A
  25 [ #L1 #k #L2 #d #e #_ #T2 #H
  26   >(lift_inv_sort1 … H) -H //
  27 | #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #d #e #HL21 #T2 #H
  28   elim (lift_inv_lref1 … H) -H * #Hid #H destruct
  29   [ elim (ldrop_trans_le … HL21 … HLK1 ?) -L1 /2 width=2/ #X #HLK2 #H
  30     elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
  31     /3 width=8/
  32   | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=8/
  33   ]
  34 | #a #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
  35   elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
  36   /4 width=4/
  37 | #a #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
  38   elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
  39   /4 width=4/
  40 | #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
  41   elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
  42   /3 width=4/
  43 | #L1 #V1 #T1 #A #_ #_ #IH1 #IH2 #L2 #d #e #HL21 #X #H
  44   elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
  45   /3 width=4/
  46 ]
  47 qed.
  48
  49 lemma aaa_inv_lift: ∀L2,T2,A. L2 ⊢ T2 ⁝ A → ∀L1,d,e. ⇩[d, e] L2 ≡ L1 →
  50                     ∀T1. ⇧[d, e] T1 ≡ T2 → L1 ⊢ T1 ⁝ A.
  51 #L2 #T2 #A #H elim H -L2 -T2 -A
  52 [ #L2 #k #L1 #d #e #_ #T1 #H
  53   >(lift_inv_sort2 … H) -H //
  54 | #I #L2 #K2 #V2 #B #i #HLK2 #_ #IHB #L1 #d #e #HL21 #T1 #H
  55   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
  56   [ elim (ldrop_conf_lt … HL21 … HLK2 ?) -L2 // -Hid /3 width=8/
  57   | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // -Hid /3 width=8/
  58   ]
  59 | #a #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
  60   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
  61   /4 width=4/
  62 | #a #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
  63   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
  64   /4 width=4/
  65 | #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
  66   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
  67   /3 width=4/
  68 | #L2 #V2 #T2 #A #_ #_ #IH1 #IH2 #L1 #d #e #HL21 #X #H
  69   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
  70   /3 width=4/
  71 ]
  72 qed-.