matita/matita/contribs/lambdadelta/basic_2A/etc/cny/cpx_cpzs.etc

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  14
  15 include "basic_2/delta_equivalence/cpzs.ma".
  16 include "basic_2/reduction/cpx.ma".
  17
  18 fact destruct_tsort_tsort: ∀k1,k2. ⋆k1 = ⋆k2 → k1 = k2.
  19 #k1 #k2 #H destruct //
  20 qed-.
  21
  22 axiom cpzs_inv_subst: ∀I,G,L,K,V1,V2,W2,i.
  23                       ⇩[i] L ≡ K.ⓑ{I}V1 → ⇧[O, i+1] V2 ≡ W2 →
  24                       ⦃G, L⦄ ⊢ #i ◆*[O, ∞] W2 → ⦃G, K⦄⊢ V1 ◆*[O, ∞] V2.
  25
  26 axiom cpzs_subst: ∀I,G,L,K,V1,V2,W2,i.
  27                   ⇩[i] L ≡ K.ⓑ{I}V1 → ⇧[O, i+1] V2 ≡ W2 →
  28                   ⦃G, K⦄⊢ V1 ◆*[O, ∞] V2 → ⦃G, L⦄ ⊢ #i ◆*[O, ∞] W2.
  29
  30 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
  31
  32 (* Forward lemmas on delta-equivalence for terms ****************************)
  33
  34 lemma cpx_fwd_cpys_cpzs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
  35                          ∀d,e. ⦃G, L⦄ ⊢ T1 ◆*[d, e] T2 ↔ ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2.
  36 #h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2
  37 [ /2 width=1 by conj/
  38 | #G #L #k #l #_ #d #e @conj #H lapply (next_lt h k)
  39   [ <(cpzs_inv_sort … H)
  40   | lapply (cpys_inv_sort1 … H) -H #H >(destruct_tsort_tsort … H)
  41   ] -H #H elim (lt_refl_false … H)
  42 | #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #d #e @conj #H
  43 (*
  44   [ @(cpys_subst … HLK … HVW2) // >yminus_Y_inj /3 width=7 by cpzs_inv_subst/
  45   | elim (cpys_inv_lref1_ldrop … H … HLK … HVW2) -H /3 width=7 by cpzs_subst/
  46   ]
  47 *)
  48 | #a #I #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e
  49   elim (IHV12 d e) -IHV12 elim (IHT12 (⫯d) e) -IHT12
  50   #IHTdx #IHTsn #IHVdx #IHVsn @conj #H
  51   [ elim (cpzs_inv_bind … H) -H /3 width=1 by cpys_bind/
  52   | elim (cpys_inv_bind1 … H) -H #X1 #X2 #H1 #H2 #H destruct /3 width=1 by cpzs_bind/
  53   ]
  54 | #I #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e
  55   elim (IHV12 d e) -IHV12 elim (IHT12 (d) e) -IHT12
  56   #IHTdx #IHTsn #IHVdx #IHVsn @conj #H
  57   [ elim (cpzs_inv_flat … H) -H /3 width=1 by cpys_flat/
  58   | elim (cpys_inv_flat1 … H) -H #X1 #X2 #H1 #H2 #H destruct /3 width=1 by cpzs_flat/
  59   ]
  60 | #G #L #V #U1 #U2 #T2 #_ #HTU2 #_ #d #e @conj #H
  61 | #G #L #V1 #T1 #T2 #_ #_ #d #e @conj #H
  62 | #G #L #V1 #V2 #T1 #HV12 #_ #d #e @conj #H
  63 | #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #d #e @conj #H
  64   [ elim (cpzs_inv_flat_bind … H)
  65   | elim (cpys_inv_flat1 … H) -H #X1 #X2 #H1 #H2 #H destruct
  66   ]
  67 | #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #d #e @conj #H
  68   [ elim (cpzs_inv_flat_bind … H)
  69   | elim (cpys_inv_flat1 … H) -H #X1 #X2 #H1 #H2 #H destruct
  70   ]
  71 ]
  72
  73