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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "static_2/relocation/drops.ma".
16 include "basic_2/rt_conversion/cpce.ma".
18 (* CONTEXT-SENSITIVE PARALLEL ETA-CONVERSION FOR TERMS **********************)
20 (* Properties with uniform slicing for local environments *******************)
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
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/
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 → ⊥) →
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/