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

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  14
  15 include "basic_2A/reduction/cpx_lift.ma".
  16 include "basic_2A/reduction/cnx.ma".
  17
  18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
  19
  20 (* Relocation properties ****************************************************)
  21
  22 lemma cnx_lift: ∀h,g,G,L0,L,T,T0,s,l,m. ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ⬇[s, l, m] L0 ≡ L →
  23                 ⬆[l, m] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡[h, g] 𝐍⦃T0⦄.
  24 #h #g #G #L0 #L #T #T0 #s #l #m #HLT #HL0 #HT0 #X #H
  25 elim (cpx_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
  26 <(HLT … HT1) in HT0; -L #HT0
  27 >(lift_mono … HT10 … HT0) -T1 -X //
  28 qed.
  29
  30 lemma cnx_inv_lift: ∀h,g,G,L0,L,T,T0,s,l,m. ⦃G, L0⦄ ⊢ ➡[h, g] 𝐍⦃T0⦄ → ⬇[s, l, m] L0 ≡ L →
  31                     ⬆[l, m] T ≡ T0 → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄.
  32 #h #g #G #L0 #L #T #T0 #s #l #m #HLT0 #HL0 #HT0 #X #H
  33 elim (lift_total X l m) #X0 #HX0
  34 lapply (cpx_lift … H … HL0 … HT0 … HX0) -L #HTX0
  35 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
  36 >(lift_inj … H … HT0) -T0 -X -l -m //
  37 qed-.