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15 include "basic_2/notation/relations/peval_3.ma".
16 include "basic_2/computation/cprs.ma".
17 include "basic_2/computation/csn.ma".
19 (* CONTEXT-SENSITIVE PARALLEL EVALUATION ON TERMS **************************)
21 definition cpre: lenv → relation term ≝
22 λL,T1,T2. L ⊢ T1 ➡* T2 ∧ L ⊢ 𝐍⦃T2⦄.
24 interpretation "context-sensitive parallel evaluation (term)"
25 'PEval L T1 T2 = (cpre L T1 T2).
27 (* Basic_properties *********************************************************)
29 (* Basic_1: was just: nf2_sn3 *)
30 lemma csn_cpre: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 → ∃T2. L ⊢ T1 ➡* 𝐍⦃T2⦄.
31 #h #g #L #T1 #H @(csn_ind … H) -T1
33 elim (cnr_dec L T1) /3 width=3/
35 elim (IHT1 … H2T1) -IHT1 -H2T1 [2: /2 width=2/ ] #T2 * /4 width=3/