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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/relocation/lifts_tdeq.ma".
  16 include "basic_2/rt_transition/cpx_drops_basic.ma".
  17 include "basic_2/rt_transition/cnx.ma".
  18
  19 (* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
  20
  21 (* Advanced inversion lemmas ************************************************)
  22
  23 lemma cnx_inv_abbr_pos (h) (G) (L): ∀V,T.  ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃+ⓓV.T⦄ → ⊥.
  24 #h #G #L #V #U1 #H
  25 elim (cpx_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
  26 elim (tdeq_dec U1 U2) #HnU12 [ -HU12 | -HTU2 ]
  27 [ elim (tdeq_inv_lifts_dx … HnU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
  28   lapply (H T1 ?) -H [ /2 width=3 by cpx_zeta/ ] #H
  29   /2 width=9 by tdeq_lifts_inv_pair_sn/
  30 | lapply (H (+ⓓV.U2) ?) -H [ /2 width=1 by cpx_bind/ ] -HU12 #H
  31   elim (tdeq_inv_pair … H) -H #_ #_ /2 width=1 by/
  32 ]
  33 qed-.