(* *)
(**************************************************************************)
+include "basic_2/notation/relations/peval_6.ma".
include "basic_2/computation/cpxs.ma".
-include "basic_2/computation/csn.ma".
+include "basic_2/computation/csx.ma".
(* CONTEXT-SENSITIVE EXTENDED PARALLEL EVALUATION ON TERMS ******************)
-definition cpxe: ∀h. sd h → lenv → relation term ≝
- λh,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 ∧ ⦃h, L⦄ ⊢ 𝐍[g]⦃T2⦄.
+definition cpxe: ∀h. sd h → relation4 genv lenv term term ≝
+ λh,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 ∧ ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T2⦄.
interpretation "context-sensitive extended parallel evaluation (term)"
- 'PEval h g L T1 T2 = (cpxe h g L T1 T2).
+ 'PEval h g G L T1 T2 = (cpxe h g G L T1 T2).
(* Basic_properties *********************************************************)
-lemma csn_cpxe: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 → ∃T2. ⦃h, L⦄ ⊢ T1 ➡*[g] 𝐍⦃T2⦄.
-#h #g #L #T1 #H @(csn_ind … H) -T1
+lemma csx_cpxe: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] 𝐍⦃T2⦄.
+#h #g #G #L #T1 #H @(csx_ind … H) -T1
#T1 #_ #IHT1
-elim (cnx_dec h g L T1) /3 width=3/
+elim (cnx_dec h g G L T1) /3 width=3/
* #T #H1T1 #H2T1
elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1 #T2 * /4 width=3/
qed-.