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

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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2A/reduction/crx_lift.ma".
  16 include "basic_2A/reduction/cix.ma".
  17
  18 (* IRREDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ***************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma cix_lref: ∀h,g,G,L,i. ⬇[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃#i⦄.
  23 #h #g #G #L #i #HL #H elim (crx_inv_lref … H) -h #I #K #V #HLK
  24 lapply (drop_mono … HLK … HL) -L -i #H destruct
  25 qed.
  26
  27 (* Properties on relocation *************************************************)
  28
  29 lemma cix_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ∀L,s,l,m. ⬇[s, l, m] L ≡ K →
  30                 ∀U. ⬆[l, m] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄.
  31 /3 width=8 by crx_inv_lift/ qed.
  32
  33 lemma cix_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄ → ∀K,s,l,m. ⬇[s, l, m] L ≡ K →
  34                     ∀T. ⬆[l, m] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
  35 /3 width=8 by crx_lift/ qed-.