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

   1 (**************************************************************************)
   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 "basic_2/rt_transition/cpx_simple.ma".
  16 include "basic_2/rt_transition/cnx.ma".
  17
  18 (* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
  19
  20 (* Inversion lemmas with simple terms ***************************************)
  21
  22 lemma cnx_inv_appl: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] ⓐV.T →
  23                     ∧∧ ❪G,L❫ ⊢ ⬈𝐍[h] V & ❪G,L❫ ⊢ ⬈𝐍[h] T & 𝐒❪T❫.
  24 #h #G #L #V1 #T1 #HVT1 @and3_intro
  25 [ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpx_pair_sn/ -HV2
  26   #H elim (teqx_inv_pair … H) -H //
  27 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpx_flat/ -HT2
  28   #H elim (teqx_inv_pair … H) -H //
  29 | generalize in match HVT1; -HVT1 elim T1 -T1 * //
  30   #p * #W1 #U1 #_ #_ #H
  31   [ elim (lifts_total V1 (𝐔❨1❩)) #V2 #HV12
  32     lapply (H (ⓓ[p]W1.ⓐV2.U1) ?) -H /2 width=3 by cpx_theta/ -HV12
  33     #H elim (teqx_inv_pair … H) -H #H destruct
  34   | lapply (H (ⓓ[p]ⓝW1.V1.U1) ?) -H /2 width=1 by cpx_beta/
  35     #H elim (teqx_inv_pair … H) -H #H destruct
  36   ]
  37 ]
  38 qed-.
  39
  40 (* Properties with simple terms *********************************************)
  41
  42 lemma cnx_appl_simple: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] V → ❪G,L❫ ⊢ ⬈𝐍[h] T → 𝐒❪T❫ →
  43                        ❪G,L❫ ⊢ ⬈𝐍[h] ⓐV.T.
  44 #h #G #L #V #T #HV #HT #HS #X #H elim (cpx_inv_appl1_simple … H) -H //
  45 #V0 #T0 #HV0 #HT0 #H destruct
  46 @teqx_pair [ @HV | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
  47 qed.