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

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  14
  15 include "basic_2A/reduction/cix.ma".
  16 include "basic_2A/reduction/cpx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
  19
  20 (* Advanced forward lemmas on irreducibility ********************************)
  21
  22 lemma cpx_fwd_cix: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T1⦄ → T2 = T1.
  23 #h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2
  24 [ //
  25 | #G #L #k #d #Hkd #H elim (cix_inv_sort … Hkd H)
  26 | #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #H
  27   elim (cix_inv_delta … HLK) //
  28 | #a * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
  29   [ elim (cix_inv_bind … H) -H #HV1 #HT1 * #H destruct
  30     lapply (IHV1 … HV1) -IHV1 -HV1 #H destruct
  31     lapply (IHT1 … HT1) -IHT1 #H destruct //
  32   | elim (cix_inv_ib2 … H) -H /3 width=2 by or_introl, eq_f2/
  33   ]
  34 | * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
  35   [ elim (cix_inv_appl … H) -H #HV1 #HT1 #_
  36     >IHV1 -IHV1 // -HV1 >IHT1 -IHT1 //
  37   | elim (cix_inv_ri2 … H) /2 width=1 by/
  38   ]
  39 | #G #L #V1 #T1 #T #T2 #_ #_ #_ #H
  40   elim (cix_inv_ri2 … H) /2 width=1 by or_introl/
  41 | #G #L #V1 #T1 #T2 #_ #_ #H
  42   elim (cix_inv_ri2 … H) /2 width=1 by/
  43 | #G #L #V1 #V2 #T #_ #_ #H
  44   elim (cix_inv_ri2 … H) /2 width=1 by/
  45 | #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #H
  46   elim (cix_inv_appl … H) -H #_ #_ #H
  47   elim (simple_inv_bind … H)
  48 | #a #G #L #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
  49   elim (cix_inv_appl … H) -H #_ #_ #H
  50   elim (simple_inv_bind … H)
  51 ]
  52 qed-.