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

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  14
  15 include "basic_2A/reduction/cpr_lift.ma".
  16 include "basic_2A/reduction/cnr.ma".
  17
  18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma cnr_lref_abst: ∀G,L,K,V,i. ⬇[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
  23 #G #L #K #V #i #HLK #X #H
  24 elim (cpr_inv_lref1 … H) -H // *
  25 #K0 #V1 #V2 #HLK0 #_ #_
  26 lapply (drop_mono … HLK … HLK0) -L #H destruct
  27 qed.
  28
  29 (* Relocation properties ****************************************************)
  30
  31 lemma cnr_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ →
  32                 ⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄.
  33 #G #L0 #L #T #T0 #s #l #m #HLT #HL0 #HT0 #X #H
  34 elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
  35 >(HLT … HT1) in HT0; -L #HT0
  36 >(lift_mono … HT10 … HT0) -T1 -X //
  37 qed.
  38
  39 lemma cnr_inv_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄ →
  40                     ⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
  41 #G #L0 #L #T #T0 #s #l #m #HLT0 #HL0 #HT0 #X #H
  42 elim (lift_total X l m) #X0 #HX0
  43 lapply (cpr_lift … H … HL0 … HT0 … HX0) -L #HTX0
  44 <(HLT0 … HTX0) in HX0; -L0 -X0 #H
  45 >(lift_inj … H … HT0) -T0 -X -s -l -m //
  46 qed-.