(* EVALUATION FOR CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION ON TERMS ****)
definition cpxe: ∀h. sd h → relation4 genv lenv term term ≝
- λh,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 â\88§ â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, o] 𝐍⦃T2⦄.
+ λh,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] T2 â\88§ â¦\83G, Lâ¦\84 â\8a¢ â¬\88[h, o] 𝐍⦃T2⦄.
interpretation "evaluation for context-sensitive extended parallel reduction (term)"
'PRedEval h o G L T1 T2 = (cpxe h o G L T1 T2).
(* Basic properties *********************************************************)
-lemma csx_cpxe: â\88\80h,o,G,L,T1. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T1 â\86\92 â\88\83T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] 𝐍⦃T2⦄.
+lemma csx_cpxe: â\88\80h,o,G,L,T1. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T1 â\86\92 â\88\83T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] 𝐍⦃T2⦄.
#h #o #G #L #T1 #H @(csx_ind … H) -T1
#T1 #_ #IHT1 elim (cnx_dec h o G L T1) /3 width=3 by ex_intro, conj/
* #T #H1T1 #H2T1 elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1