matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_simple.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 "basic_2/rt_transition/cpm_simple.ma".
  16 include "basic_2/rt_transition/cnr.ma".
  17
  18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE R-TRANSITION **************************)
  19
  20 (* Inversion lemmas with simple terms ***************************************)
  21
  22 lemma cnr_inv_appl (h) (G) (L):
  23       ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] ⓐV.T →
  24       ∧∧ ❪G,L❫ ⊢ ➡𝐍[h,0] V & ❪G,L❫ ⊢ ➡𝐍[h,0] T & 𝐒❪T❫.
  25 #h #G #L #V1 #T1 #HVT1 @and3_intro
  26 [ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpr_pair_sn/ -HV2 #H destruct //
  27 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpr_flat/ -HT2 #H destruct //
  28 | generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
  29   [ elim (lifts_total V1 𝐔❨1❩) #V2 #HV12
  30     lapply (H (ⓓ[a]W1.ⓐV2.U1) ?) -H /2 width=3 by cpm_theta/ -HV12 #H destruct
  31   | lapply (H (ⓓ[a]ⓝW1.V1.U1) ?) -H /2 width=1 by cpm_beta/ #H destruct
  32   ]
  33 ]
  34 qed-.
  35
  36 (* Properties with simple terms *********************************************)
  37
  38 (* Basic_1: was only: nf2_appl_lref *)
  39 lemma cnr_appl_simple (h) (G) (L):
  40       ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] V → ❪G,L❫ ⊢ ➡𝐍[h,0] T → 𝐒❪T❫ → ❪G,L❫ ⊢ ➡𝐍[h,0] ⓐV.T.
  41 #h #G #L #V #T #HV #HT #HS #X #H
  42 elim (cpm_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
  43 <(HV … HV0) -V0 <(HT … HT0) -T0 //
  44 qed.