matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_fqus.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 "static_2/s_computation/fqus_fqup.ma".
  16 include "basic_2/dynamic/cnv_drops.ma".
  17
  18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  19
  20 (* Properties with supclosure ***********************************************)
  21
  22 (* Basic_2A1: uses: snv_fqu_conf *)
  23 lemma cnv_fqu_conf (h) (a):
  24       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂ ❪G2,L2,T2❫ →
  25       ❪G1,L1❫ ⊢ T1 ![h,a] → ❪G2,L2❫ ⊢ T2 ![h,a].
  26 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  27 [ #I1 #G1 #L1 #V1 #H
  28   elim (cnv_inv_zero … H) -H #I2 #L2 #V2 #HV2 #H destruct //
  29 | * [ #p #I1 | * ] #G1 #L1 #V1 #T1 #H
  30   [ elim (cnv_inv_bind … H) -H //
  31   | elim (cnv_inv_appl … H) -H //
  32   | elim (cnv_inv_cast … H) -H //
  33   ]
  34 | #p #I1 #G1 #L1 #V1 #T1 #_ #H
  35   elim (cnv_inv_bind … H) -H //
  36 | #p #I1 #G1 #L1 #V1 #T1 #H destruct
  37 | * #G1 #L1 #V1 #T1 #H
  38   [ elim (cnv_inv_appl … H) -H //
  39   | elim (cnv_inv_cast … H) -H //
  40   ]
  41 | #I1 #G1 #L1 #T1 #U1 #HTU1 #HU
  42   /4 width=7 by cnv_inv_lifts, drops_refl, drops_drop/
  43 ]
  44 qed-.
  45
  46 (* Basic_2A1: uses: snv_fquq_conf *)
  47 lemma cnv_fquq_conf (h) (a):
  48       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮ ❪G2,L2,T2❫ →
  49       ❪G1,L1❫ ⊢ T1 ![h,a] → ❪G2,L2❫ ⊢ T2 ![h,a].
  50 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [|*]
  51 /2 width=5 by cnv_fqu_conf/
  52 qed-.
  53
  54 (* Basic_2A1: uses: snv_fqup_conf *)
  55 lemma cnv_fqup_conf (h) (a):
  56       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂+ ❪G2,L2,T2❫ →
  57       ❪G1,L1❫ ⊢ T1 ![h,a] → ❪G2,L2❫ ⊢ T2 ![h,a].
  58 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
  59 /3 width=5 by fqup_strap1, cnv_fqu_conf/
  60 qed-.
  61
  62 (* Basic_2A1: uses: snv_fqus_conf *)
  63 lemma cnv_fqus_conf (h) (a):
  64       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂* ❪G2,L2,T2❫ →
  65       ❪G1,L1❫ ⊢ T1 ![h,a] → ❪G2,L2❫ ⊢ T2 ![h,a].
  66 #h #a #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H [|*]
  67 /2 width=5 by cnv_fqup_conf/
  68 qed-.