matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_drops.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/relocation/lifts_tweq.ma".
  16 include "basic_2/rt_computation/cpms_drops.ma".
  17 include "basic_2/rt_computation/cnuw.ma".
  18
  19 (* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
  20
  21 (* Properties with generic relocation ***************************************)
  22
  23 lemma cnuw_lifts (h) (G): d_liftable1 … (cnuw h G).
  24 #h #G #K #T #HT #b #f #L #HLK #U #HTU #n #U0 #H
  25 elim (cpms_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
  26 lapply (HT … HT0) -G -K /2 width=6 by tweq_lifts_bi/
  27 qed-.
  28
  29 (* Inversion lemmas with generic relocation *********************************)
  30
  31 lemma cnuw_inv_lifts (h) (G): d_deliftable1 … (cnuw h G).
  32 #h #G #L #U #HU #b #f #K #HLK #T #HTU #n #T0 #H
  33 elim (cpms_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
  34 lapply (HU … HU0) -G -L /2 width=6 by tweq_inv_lifts_bi/
  35 qed-.
  36
  37 (* Advanced properties ******************************************************)
  38
  39 lemma cnuw_lref (h) (I) (G) (L):
  40       ∀i. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] #i → ❪G,L.ⓘ[I]❫ ⊢ ➡𝐍𝐖*[h] #↑i.
  41 #h #I #G #L #i #Hi #n #X2 #H
  42 elim (cpms_inv_lref_sn … H) -H *
  43 [ #H #_ destruct //
  44 | #T2 #HT2 #HTX2
  45   lapply (Hi … HT2) -Hi -HT2 #H
  46   lapply (tweq_inv_lref_sn … H) -H #H destruct
  47   lapply (lifts_inv_lref1_uni … HTX2) -HTX2 #H destruct //
  48 ]
  49 qed.
  50
  51 lemma cnuw_atom_drops (h) (b) (G) (L):
  52       ∀i. ⇩*[b,𝐔❨i❩] L ≘ ⋆ → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] #i.
  53 #h #b #G #L #i #Hi #n #X #H
  54 elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #K #V1 #V2 #HLK
  55 lapply (drops_gen b … HLK) -HLK #HLK
  56 lapply (drops_mono … Hi … HLK) -L #H destruct
  57 qed.
  58
  59 lemma cnuw_unit_drops (h) (I) (G) (L):
  60       ∀K,i. ⇩*[i] L ≘ K.ⓤ[I] → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] #i.
  61 #h #I #G #L #K #i #HLK #n #X #H
  62 elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #Y #V1 #V2 #HLY
  63 lapply (drops_mono … HLK … HLY) -L #H destruct
  64 qed.