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

   1 (**************************************************************************)
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  14
  15 include "basic_2/rt_transition/cnr.ma".
  16 include "basic_2/rt_transition/cnu.ma".
  17
  18 (* NORMAL TERMS FOR T-UNUNBOUND RT-TRANSITION *******************************)
  19
  20 (* Advanced properties with normal terms for r-transition *******************)
  21
  22 lemma cnu_abst (h) (p) (G) (L):
  23       ∀W. ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃W⦄ → ∀T.⦃G,L.ⓛW⦄ ⊢ ⥲[h] 𝐍⦃T⦄ → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃ⓛ{p}W.T⦄.
  24 #h #p #G #L #W1 #HW1 #T1 #HT1 #n #X #H
  25 elim (cpm_inv_abst1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct
  26 <(HW1 … HW12) -W2 /3 width=2 by tueq_bind/
  27 qed.
  28
  29 lemma cnu_abbr_neg (h) (G) (L):
  30       ∀V. ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃V⦄ → ∀T.⦃G,L.ⓓV⦄ ⊢ ⥲[h] 𝐍⦃T⦄ → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃-ⓓV.T⦄.
  31 #h #G #L #V1 #HV1 #T1 #HT1 #n #X #H
  32 elim (cpm_inv_abbr1 … H) -H *
  33 [ #V2 #T2 #HV12 #HT12 #H destruct
  34   <(HV1 … HV12) -V2 /3 width=2 by tueq_bind/
  35 | #X1 #_ #_ #H destruct
  36 ]
  37 qed.