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15 include "basic_2/notation/relations/predeval_4.ma".
16 include "basic_2/computation/cprs.ma".
17 include "basic_2/computation/csx.ma".
19 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS *************)
21 definition cpre: relation4 genv lenv term term ≝
22 λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 ∧ ⦃G, L⦄ ⊢ ➡ 𝐍⦃T2⦄.
24 interpretation "evaluation for context-sensitive parallel reduction (term)"
25 'PRedEval G L T1 T2 = (cpre G L T1 T2).
27 (* Basic_properties *********************************************************)
29 (* Basic_1: was just: nf2_sn3 *)
30 lemma csx_cpre: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡* 𝐍⦃T2⦄.
31 #h #g #G #L #T1 #H @(csx_ind … H) -T1
32 #T1 #_ #IHT1 elim (cnr_dec G L T1) /3 width=3 by ex_intro, conj/
33 * #T #H1T1 #H2T1 elim (IHT1 … H2T1) -IHT1 -H2T1 /2 width=2 by cpr_cpx/
34 #T2 * /4 width=3 by cprs_strap2, ex_intro, conj/