matita/matita/contribs/lambdadelta/basic_2A/reduction/cnx_crx.ma

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  14
  15 include "basic_2A/reduction/crx.ma".
  16 include "basic_2A/reduction/cnx.ma".
  17
  18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
  19
  20 (* Advanced inversion lemmas on reducibility ********************************)
  21
  22 (* Note: this property is unusual *)
  23 lemma cnx_inv_crx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ⊥.
  24 #h #g #G #L #T #H elim H -L -T
  25 [ #L #k #d #Hkd #H
  26   lapply (cnx_inv_sort … H) -H #H
  27   lapply (deg_mono … H Hkd) -h -L -k <plus_n_Sm #H destruct
  28 | #I #L #K #V #i #HLK #H
  29   elim (cnx_inv_delta … HLK H)
  30 | #L #V #T #_ #IHV #H
  31   elim (cnx_inv_appl … H) -H /2 width=1 by/
  32 | #L #V #T #_ #IHT #H
  33   elim (cnx_inv_appl … H) -H /2 width=1 by/
  34 | #I #L #V #T * #H1 #H2 destruct
  35   [ elim (cnx_inv_zeta … H2)
  36   | elim (cnx_inv_eps … H2)
  37   ]
  38 |6,7: #a * [ elim a ] #L #V #T * #H1 #_ #IH #H2 destruct
  39   [1,3: elim (cnx_inv_abbr … H2) -H2 /2 width=1 by/
  40   |*: elim (cnx_inv_abst … H2) -H2 /2 width=1 by/
  41   ]
  42 | #a #L #V #W #T #H
  43   elim (cnx_inv_appl … H) -H #_ #_ #H
  44   elim (simple_inv_bind … H)
  45 | #a #L #V #W #T #H
  46   elim (cnx_inv_appl … H) -H #_ #_ #H
  47   elim (simple_inv_bind … H)
  48 ]
  49 qed-.