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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "ground_2/relocation/rtmap_id.ma".
16 include "static_2/notation/relations/subseteq_4.ma".
17 include "static_2/syntax/lveq.ma".
18 include "static_2/static/frees.ma".
20 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
22 definition fsle: 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 = (fsle L1 T1 L2 T2).
29 interpretation "free variables inclusion (term)"
30 'subseteq T1 T2 = (fsle LAtom T1 LAtom T2).
32 (* Basic properties *********************************************************)
34 lemma fsle_sort: ∀L,s1,s2. ⦃L,⋆s1⦄ ⊆ ⦃L,⋆s2⦄.
35 /3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
37 lemma fsle_gref: ∀L,l1,l2. ⦃L,§l1⦄ ⊆ ⦃L,§l2⦄.
38 /3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.