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:                                           *)
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  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 (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
  24                             ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
  25 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  26 [ #I1 #G1 #L1 #V1 #H
  27   elim (cnv_inv_zero … H) -H #I2 #L2 #V2 #HV2 #H destruct //
  28 | * [ #p #I1 | * ] #G1 #L1 #V1 #T1 #H
  29   [ elim (cnv_inv_bind … H) -H //
  30   | elim (cnv_inv_appl … H) -H //
  31   | elim (cnv_inv_cast … H) -H //
  32   ]
  33 | #p #I1 #G1 #L1 #V1 #T1 #H
  34   elim (cnv_inv_bind … H) -H //
  35 | #p #I1 #G1 #L1 #V1 #T1 #H destruct
  36 | * #G1 #L1 #V1 #T1 #H
  37   [ elim (cnv_inv_appl … H) -H //
  38   | elim (cnv_inv_cast … H) -H //
  39   ]
  40 | #I1 #G1 #L1 #T1 #U1 #HTU1 #HU
  41   /4 width=7 by cnv_inv_lifts, drops_refl, drops_drop/
  42 ]
  43 qed-.
  44
  45 (* Basic_2A1: uses: snv_fquq_conf *)
  46 lemma cnv_fquq_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
  47                              ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
  48 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [|*]
  49 /2 width=5 by cnv_fqu_conf/
  50 qed-.
  51
  52 (* Basic_2A1: uses: snv_fqup_conf *)
  53 lemma cnv_fqup_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
  54                              ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
  55 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
  56 /3 width=5 by fqup_strap1, cnv_fqu_conf/
  57 qed-.
  58
  59 (* Basic_2A1: uses: snv_fqus_conf *)
  60 lemma cnv_fqus_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
  61                              ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
  62 #a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H [|*]
  63 /2 width=5 by cnv_fqup_conf/
  64 qed-.