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 (* Basic_1: was: nf2_lref_abst *)
  23 lemma cnr_lref_abst: ∀G,L,K,V,i. ⬇[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
  24 #G #L #K #V #i #HLK #X #H
  25 elim (cpr_inv_lref1 … H) -H // *
  26 #K0 #V1 #V2 #HLK0 #_ #_
  27 lapply (drop_mono … HLK … HLK0) -L #H destruct
  28 qed.
  29
  30 (* Relocation properties ****************************************************)
  31
  32 (* Basic_1: was: nf2_lift *)
  33 lemma cnr_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ →
  34                 ⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄.
  35 #G #L0 #L #T #T0 #s #l #m #HLT #HL0 #HT0 #X #H
  36 elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
  37 <(HLT … HT1) in HT0; -L #HT0
  38 >(lift_mono … HT10 … HT0) -T1 -X //
  39 qed.
  40
  41 (* Note: this was missing in basic_1 *)
  42 lemma cnr_inv_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄ →
  43                     ⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
  44 #G #L0 #L #T #T0 #s #l #m #HLT0 #HL0 #HT0 #X #H
  45 elim (lift_total X l m) #X0 #HX0
  46 lapply (cpr_lift … H … HL0 … HT0 … HX0) -L #HTX0
  47 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
  48 >(lift_inj … H … HT0) -T0 -X -s -l -m //
  49 qed-.