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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground_2/relocation/rtmap_id.ma".
16 include "basic_2/notation/relations/subseteq_4.ma".
17 include "basic_2/syntax/lveq.ma".
18 include "basic_2/static/frees.ma".
20 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
22 definition fle: bi_relation lenv term ≝ λL1,T1,L2,T2.
23 ∃∃n1,n2,f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 &
24 L1 ≋ⓧ*[n1, n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
26 interpretation "free variables inclusion (restricted closure)"
27 'SubSetEq L1 T1 L2 T2 = (fle L1 T1 L2 T2).
29 (* Basic properties *********************************************************)
31 lemma fle_sort: ∀L,s1,s2. ⦃L, ⋆s1⦄ ⊆ ⦃L, ⋆s2⦄.
32 /3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
34 lemma fle_gref: ∀L,l1,l2. ⦃L, §l1⦄ ⊆ ⦃L, §l2⦄.
35 /3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.