(* Basic_2A1: uses: scpes *)
definition cpes (h) (n1) (n2): relation4 genv lenv term term ≝
λG,L,T1,T2.
- ∃∃T. ⦃G, L⦄ ⊢ T1 ➡*[n1,h] T & ⦃G, L⦄ ⊢ T2 ➡*[n2,h] T.
+ ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[n1,h] T & ⦃G,L⦄ ⊢ T2 ➡*[n2,h] 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):
- ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡*[n1,h] T →
- ∀T2. ⦃G, L⦄ ⊢ T2 ➡*[n2,h] T → ⦃G, L⦄ ⊢ T1 ⬌*[h,n1,n2] T2.
+ ∀G,L,T1,T. ⦃G,L⦄ ⊢ T1 ➡*[n1,h] T →
+ ∀T2. ⦃G,L⦄ ⊢ T2 ➡*[n2,h] T → ⦃G,L⦄ ⊢ 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):
- ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌*[h,n1,n2] T2 → ⦃G, L⦄ ⊢ T2 ⬌*[h,n2,n1] T1.
+ ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬌*[h,n1,n2] T2 → ⦃G,L⦄ ⊢ T2 ⬌*[h,n2,n1] T1.
#h #n1 #n2 #G #L #T1 #T2 * /2 width=3 by cpms_div/
qed-.