matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnu_drops.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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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/relocation/lifts_tueq.ma".
  16 include "basic_2/rt_transition/cpm_drops.ma".
  17 include "basic_2/rt_transition/cnu.ma".
  18
  19 (* NORMAL TERMS FOR T-UNUNBOUND RT-TRANSITION *******************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma cnu_atom_drops (h) (b) (G) (L):
  24       ∀i. ⬇*[b,𝐔❴i❵] L ≘ ⋆ → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃#i⦄.
  25 #h #b #G #L #i #Hi #n #X #H
  26 elim (cpm_inv_lref1_drops … H) -H * [ // || #m ] #K #V1 #V2 #HLK
  27 lapply (drops_gen b … HLK) -HLK #HLK
  28 lapply (drops_mono … Hi … HLK) -L #H destruct
  29 qed.
  30
  31 lemma cnu_unit_drops (h) (I) (G) (L):
  32       ∀K,i. ⬇*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃#i⦄.
  33 #h #I #G #L #K #i #HLK #n #X #H
  34 elim (cpm_inv_lref1_drops … H) -H * [ // || #m ] #Y #V1 #V2 #HLY
  35 lapply (drops_mono … HLK … HLY) -L #H destruct
  36 qed.
  37
  38 (* Properties with generic relocation ***************************************)
  39
  40 lemma cnu_lifts (h) (G): d_liftable1 … (cnu h G).
  41 #h #G #K #T #HT #b #f #L #HLK #U #HTU #n #U0 #H
  42 elim (cpm_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
  43 lapply (HT … HT0) -G -K /2 width=6 by tueq_lifts_bi/
  44 qed-.
  45
  46 (* Inversion lemmas with generic relocation *********************************)
  47
  48 lemma cnu_inv_lifts (h) (G): d_deliftable1 … (cnu h G).
  49 #h #G #L #U #HU #b #f #K #HLK #T #HTU #n #T0 #H
  50 elim (cpm_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
  51 lapply (HU … HU0) -G -L /2 width=6 by tueq_inv_lifts_bi/
  52 qed-.