(* *)
(**************************************************************************)
-include "ground_2/relocation/rtmap_id.ma".
+include "ground/xoa/ex_4_4.ma".
+include "ground/relocation/rtmap_id.ma".
include "static_2/notation/relations/subseteq_4.ma".
include "static_2/syntax/lveq.ma".
include "static_2/static/frees.ma".
(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
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.
+ ∃∃n1,n2,f1,f2. L1 ⊢ 𝐅+❪T1❫ ≘ f1 & L2 ⊢ 𝐅+❪T2❫ ≘ 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: â\88\80L,s1,s2. â¦\83L,â\8b\86s1â¦\84 â\8a\86 â¦\83L,â\8b\86s2â¦\84.
-/3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
+lemma fsle_sort: â\88\80L,s1,s2. â\9dªL,â\8b\86s1â\9d« â\8a\86 â\9dªL,â\8b\86s2â\9d«.
+/3 width=8 by frees_sort, pr_sle_refl, ex4_4_intro/ qed.
-lemma fsle_gref: â\88\80L,l1,l2. â¦\83L,§l1â¦\84 â\8a\86 â¦\83L,§l2â¦\84.
-/3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.
+lemma fsle_gref: â\88\80L,l1,l2. â\9dªL,§l1â\9d« â\8a\86 â\9dªL,§l2â\9d«.
+/3 width=8 by frees_gref, pr_sle_refl, ex4_4_intro/ qed.