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15 include "basic_2/notation/relations/predeval_6.ma".
16 include "basic_2/computation/cpxs.ma".
17 include "basic_2/computation/csx.ma".
19 (* EVALUATION FOR CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION ON TERMS ****)
21 definition cpxe: ∀h. sd h → relation4 genv lenv term term ≝
22 λh,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2 ∧ ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T2⦄.
24 interpretation "evaluation for context-sensitive extended parallel reduction (term)"
25 'PRedEval h o G L T1 T2 = (cpxe h o G L T1 T2).
27 (* Basic properties *********************************************************)
29 lemma csx_cpxe: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, o] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ⬈*[h, o] 𝐍⦃T2⦄.
30 #h #o #G #L #T1 #H @(csx_ind … H) -T1
31 #T1 #_ #IHT1 elim (cnx_dec h o G L T1) /3 width=3 by ex_intro, conj/
32 * #T #H1T1 #H2T1 elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1
33 #T2 * /4 width=3 by cpxs_strap2, ex_intro, conj/