definition fsle: bi_relation lenv term ≝ λL1,T1,L2,T2.
∃∃n1,n2,f1,f2. L1 ⊢ 𝐅+❪T1❫ ≘ f1 & L2 ⊢ 𝐅+❪T2❫ ≘ f2 &
- L1 â\89\8bâ\93§*[n1,n2] L2 & ⫱*[n1]f1 â\8a\86 ⫱*[n2]f2.
+ L1 â\89\8bâ\93§*[n1,n2] L2 & â«°*[n1]f1 â\8a\86 â«°*[n2]f2.
interpretation "free variables inclusion (restricted closure)"
'SubSetEq L1 T1 L2 T2 = (fsle L1 T1 L2 T2).
(* Basic properties *********************************************************)
lemma fsle_sort: ∀L,s1,s2. ❪L,⋆s1❫ ⊆ ❪L,⋆s2❫.
-/3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
+/3 width=8 by frees_sort, pr_sle_refl, ex4_4_intro/ qed.
lemma fsle_gref: ∀L,l1,l2. ❪L,§l1❫ ⊆ ❪L,§l2❫.
-/3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.
+/3 width=8 by frees_gref, pr_sle_refl, ex4_4_intro/ qed.