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

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  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❫ ⊢ ➡[h] 𝐍❪ⓐV.T❫ → ∧∧ ❪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 cpr_pair_sn/ -HV2 #H destruct //
  26 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpr_flat/ -HT2 #H destruct //
  27 | generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
  28   [ elim (lifts_total V1 𝐔❨1❩) #V2 #HV12
  29     lapply (H (ⓓ[a]W1.ⓐV2.U1) ?) -H /2 width=3 by cpm_theta/ -HV12 #H destruct
  30   | lapply (H (ⓓ[a]ⓝW1.V1.U1) ?) -H /2 width=1 by cpm_beta/ #H destruct
  31   ]
  32 ]
  33 qed-.
  34
  35 (* Properties with simple terms *********************************************)
  36
  37 (* Basic_1: was only: nf2_appl_lref *)
  38 lemma cnr_appl_simple (h) (G) (L):
  39       ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪V❫ → ❪G,L❫ ⊢ ➡[h] 𝐍❪T❫ → 𝐒❪T❫ → ❪G,L❫ ⊢ ➡[h] 𝐍❪ⓐV.T❫.
  40 #h #G #L #V #T #HV #HT #HS #X #H
  41 elim (cpm_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
  42 <(HV … HV0) -V0 <(HT … HT0) -T0 //
  43 qed.