(* Basic_2A1: uses: scpes *)
definition cpes (h) (n1) (n2): relation4 genv lenv term term ≝
λG,L,T1,T2.
- â\88\83â\88\83T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n1,h] T & â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡*[n2,h] T.
+ â\88\83â\88\83T. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n1] T & â\9d¨G,Lâ\9d© â\8a¢ T2 â\9e¡*[h,n2] T.
interpretation "t-bound context-sensitive parallel rt-equivalence (term)"
'PConvStar h n1 n2 G L T1 T2 = (cpes h n1 n2 G L T1 T2).
(* Basic_2A1: uses: scpds_div *)
lemma cpms_div (h) (n1) (n2):
- â\88\80G,L,T1,T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n1,h] T →
- â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡*[n2,h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h,n1,n2] T2.
+ â\88\80G,L,T1,T. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n1] T →
+ â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T2 â\9e¡*[h,n2] T â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ⬌*[h,n1,n2] T2.
/2 width=3 by ex2_intro/ qed.
lemma cpes_refl (h): ∀G,L. reflexive … (cpes h 0 0 G L).
(* Basic_2A1: uses: scpes_sym *)
lemma cpes_sym (h) (n1) (n2):
- â\88\80G,L,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\8c*[h,n1,n2] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 ⬌*[h,n2,n1] T1.
+ â\88\80G,L,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\8c*[h,n1,n2] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T2 ⬌*[h,n2,n1] T1.
#h #n1 #n2 #G #L #T1 #T2 * /2 width=3 by cpms_div/
qed-.