matita/matita/contribs/lambdadelta/basic_2/reduction/cnr_lift.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/reduction/cpr_lift.ma".
  16 include "basic_2/reduction/cnr.ma".
  17
  18 (* CONTEXT-SENSITIVE NORMAL TERMS *******************************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 (* Basic_1: was only: nf2_csort_lref *)
  23 lemma cnr_lref_atom: ∀L,i. ⇩[0, i] L ≡ ⋆ → L ⊢ 𝐍⦃#i⦄.
  24 #L #i #HL #X #H
  25 elim (cpr_inv_lref1 … H) -H // *
  26 #K #V1 #V2 #HLK #_ #_
  27 lapply (ldrop_mono … HL … HLK) -L #H destruct
  28 qed.
  29
  30 (* Basic_1: was: nf2_lref_abst *)
  31 lemma cnr_lref_abst: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓛV → L ⊢ 𝐍⦃#i⦄.
  32 #L #K #V #i #HLK #X #H
  33 elim (cpr_inv_lref1 … H) -H // *
  34 #K0 #V1 #V2 #HLK0 #_ #_
  35 lapply (ldrop_mono … HLK … HLK0) -L #H destruct
  36 qed.
  37
  38 (* Relocation properties ****************************************************)
  39
  40 (* Basic_1: was: nf2_lift *)
  41 lemma cnr_lift: ∀L0,L,T,T0,d,e.
  42                 L ⊢ 𝐍⦃T⦄ → ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → L0 ⊢ 𝐍⦃T0⦄.
  43 #L0 #L #T #T0 #d #e #HLT #HL0 #HT0 #X #H
  44 elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
  45 <(HLT … HT1) in HT0; -L #HT0
  46 >(lift_mono … HT10 … HT0) -T1 -X //
  47 qed.
  48
  49 (* Note: this was missing in basic_1 *)
  50 lemma cnr_inv_lift: ∀L0,L,T,T0,d,e.
  51                     L0 ⊢ 𝐍⦃T0⦄ → ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → L ⊢ 𝐍⦃T⦄.
  52 #L0 #L #T #T0 #d #e #HLT0 #HL0 #HT0 #X #H
  53 elim (lift_total X d e) #X0 #HX0
  54 lapply (cpr_lift … H … HL0 … HT0 … HX0) -L #HTX0
  55 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
  56 >(lift_inj … H … HT0) -T0 -X -d -e //
  57 qed-.