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

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  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⦄ ⊢ ⬈[h] 𝐍⦃ⓐV.T⦄ →
  23                     ∧∧ ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃V⦄ & ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃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 (tdeq_inv_pair … H) -H //
  27 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpx_flat/ -HT2
  28   #H elim (tdeq_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 (tdeq_inv_pair … H) -H #H destruct
  34   | lapply (H (ⓓ{p}ⓝW1.V1.U1) ?) -H /2 width=1 by cpx_beta/
  35     #H elim (tdeq_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⦄ ⊢ ⬈[h] 𝐍⦃V⦄ → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ → 𝐒⦃T⦄ →
  43                        ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃ⓐ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 @tdeq_pair [ @HV | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
  47 qed.