include "ground_2/relocation/rtmap_id.ma".
include "basic_2/notation/relations/subseteq_4.ma".
-include "basic_2/syntax/voids.ma".
+include "basic_2/syntax/lveq.ma".
include "basic_2/static/frees.ma".
(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
definition fle: bi_relation lenv term ≝ λL1,T1,L2,T2.
∃∃n1,n2,f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 &
- ⓧ*[n1]L1 ≋ ⓧ*[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 = (fle L1 T1 L2 T2).
(* Basic properties *********************************************************)
lemma fle_sort: ∀L,s1,s2. ⦃L, ⋆s1⦄ ⊆ ⦃L, ⋆s2⦄.
-#L elim (voids_refl L)
+#L elim (lveq_refl L)
/3 width=8 by frees_sort, sle_refl, ex4_4_intro/
qed.
lemma fle_gref: ∀L,l1,l2. ⦃L, §l1⦄ ⊆ ⦃L, §l2⦄.
-#L elim (voids_refl L)
+#L elim (lveq_refl L)
/3 width=8 by frees_gref, sle_refl, ex4_4_intro/
qed.