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

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/reduction/cpx_lift.ma".
  16 include "basic_2/reduction/cnx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED NORMAL TERMS **********************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma cnx_lref_atom: ∀h,g,L,i. ⇩[0, i] L ≡ ⋆ → ⦃h, L⦄ ⊢ 𝐍[g]⦃#i⦄.
  23 #h #g #L #i #HL #X #H
  24 elim (cpx_inv_lref1 … H) -H // *
  25 #I #K #V1 #V2 #HLK #_ #_
  26 lapply (ldrop_mono … HL … HLK) -L #H destruct
  27 qed.
  28
  29 (* Relocation properties ****************************************************)
  30
  31 lemma cnx_lift: ∀h,g,L0,L,T,T0,d,e. ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ → ⇩[d, e] L0 ≡ L →
  32                 ⇧[d, e] T ≡ T0 → ⦃h, L0⦄ ⊢ 𝐍[g]⦃T0⦄.
  33 #h #g #L0 #L #T #T0 #d #e #HLT #HL0 #HT0 #X #H
  34 elim (cpx_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 cnx_inv_lift: ∀h,g,L0,L,T,T0,d,e. ⦃h, L0⦄ ⊢ 𝐍[g]⦃T0⦄ → ⇩[d, e] L0 ≡ L →
  40                     ⇧[d, e] T ≡ T0 → ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄.
  41 #h #g #L0 #L #T #T0 #d #e #HLT0 #HL0 #HT0 #X #H
  42 elim (lift_total X d e) #X0 #HX0
  43 lapply (cpx_lift … H … HL0 … HT0 … HX0) -L #HTX0
  44 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
  45 >(lift_inj … H … HT0) -T0 -X -d -e //
  46 qed-.