matita/matita/contribs/lambdadelta/basic_2/rt_conversion/cpce_drops.ma

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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "static_2/relocation/drops.ma".
  16 include "basic_2/rt_conversion/cpce.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL ETA-CONVERSION FOR TERMS **********************)
  19
  20 (* Properties with uniform slicing for local environments *******************)
  21
  22 lemma cpce_eta_drops (h) (n) (G) (K):
  23       ∀p,W,V1,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U →
  24       ∀V2. ⦃G,K⦄ ⊢ V1 ⬌η[h] V2 →
  25       ∀i,L. ⇩*[i] L ≘ K.ⓛW →
  26       ∀W2. ⇧*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ⬌η[h] +ⓛW2.ⓐ#0.#↑i.
  27 #h #n #G #K #p #W #V1 #U #HWU #V2 #HV12 #i elim i -i
  28 [ #L #HLK #W2 #HVW2
  29   >(drops_fwd_isid … HLK) -L [| // ] /2 width=8 by cpce_eta/
  30 | #i #IH #L #HLK #W2 #HVW2
  31   elim (drops_inv_succ … HLK) -HLK #I #Y #HYK #H destruct
  32   elim (lifts_split_trans … HVW2 (𝐔❴↑i❵) (𝐔❴1❵)) [| // ] #X2 #HVX2 #HXW2
  33   /5 width=7 by cpce_lref, lifts_push_lref, lifts_bind, lifts_flat/
  34 ]
  35 qed.
  36
  37 lemma cpce_zero_drops (h) (G):
  38       ∀i,L. (∀n,p,K,W,V,U. ⇩*[i] L ≘ K.ⓛW → ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V.U → ⊥) →
  39       ⦃G,L⦄ ⊢ #i ⬌η[h] #i.
  40 #h #G #i elim i -i
  41 [ * [ #_ // ] #L #I #Hi
  42   /4 width=8 by cpce_zero, drops_refl/
  43 | #i #IH * [ -IH #_ // ] #L #I #Hi
  44   /5 width=8 by cpce_lref, drops_drop/
  45 ]
  46 qed.