definition fsle: bi_relation lenv term ≝ λL1,T1,L2,T2.
∃∃n1,n2,f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≘ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≘ f2 &
- L1 ≋ⓧ*[n1, n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
+ L1 ≋ⓧ*[n1,n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[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⦄.
+lemma fsle_sort: ∀L,s1,s2. ⦃L,⋆s1⦄ ⊆ ⦃L,⋆s2⦄.
/3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
-lemma fsle_gref: ∀L,l1,l2. ⦃L, §l1⦄ ⊆ ⦃L, §l2⦄.
+lemma fsle_gref: ∀L,l1,l2. ⦃L,§l1⦄ ⊆ ⦃L,§l2⦄.
/3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.