(* CONTEXT-SENSITIVE PARALLEL EVALUATION ON TERMS **************************)
definition cpe: lenv → relation term ≝
- λL,T1,T2. L ⊢ T1 ➡* T2 ∧ L ⊢ 𝐍[T2].
+ λL,T1,T2. L ⊢ T1 ➡* T2 ∧ L ⊢ 𝐍⦃T2⦄.
interpretation "context-sensitive parallel evaluation (term)"
'PEval L T1 T2 = (cpe L T1 T2).
(* Basic_properties *********************************************************)
(* Basic_1: was: nf2_sn3 *)
-lemma cpe_csn: ∀L,T1. L ⊢ ⬇* T1 → ∃T2. L ⊢ T1 ➡* 𝐍[T2].
+lemma cpe_csn: ∀L,T1. L ⊢ ⬇* T1 → ∃T2. L ⊢ T1 ➡* 𝐍⦃T2⦄.
#L #T1 #H @(csn_ind … H) -T1
#T1 #_ #IHT1
elim (cnf_dec L T1) /3 width=3/