(* Basic_2A1: uses: cprre *)
definition cpmre (h) (n) (G) (L): relation2 term term ≝
- λT1,T2. â\88§â\88§ â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 & â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83T2â¦\84.
+ λT1,T2. â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n,h] T2 & â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] ð\9d\90\8dâ\9dªT2â\9d«.
interpretation "evaluation for t-bound context-sensitive parallel rt-transition (term)"
'PRedEval h n G L T1 T2 = (cpmre h n G L T1 T2).
(* Basic properties *********************************************************)
lemma cpmre_intro (h) (n) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83T2â¦\84 â\86\92 â¦\83G,Lâ¦\84â\8a¢T1â\9e¡*[h,n]ð\9d\90\8dâ¦\83T2â¦\84.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] ð\9d\90\8dâ\9dªT2â\9d« â\86\92 â\9dªG,Lâ\9d«â\8a¢T1â\9e¡*[h,n]ð\9d\90\8dâ\9dªT2â\9d«.
/2 width=1 by conj/ qed.
(* Basic forward lemmas *****************************************************)
lemma cpmre_fwd_cpms (h) (n) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84â\8a¢T1â\9e¡*[h,n]ð\9d\90\8dâ¦\83T2â¦\84 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2.
+ â\88\80T1,T2. â\9dªG,Lâ\9d«â\8a¢T1â\9e¡*[h,n]ð\9d\90\8dâ\9dªT2â\9d« â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2.
#h #n #G #L #T1 #T2 * //
qed-.