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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 "basic_2/static/lfxs_length.ma".
16 include "basic_2/static/lfxs_fsle.ma".
17 include "basic_2/static/lfeq.ma".
19 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
21 (* Properties with free variables inclusion for restricted closures *********)
23 lemma lfeq_fsle_comp: lfxs_fsle_compatible ceq.
25 elim (frees_total L1 T)
26 /4 width=8 by frees_lfeq_conf, lfxs_fwd_length, lveq_length_eq, sle_refl, ex4_4_intro/
29 (* Forward lemmas with free variables inclusion for restricted closures *****)
31 lemma lfeq_lfxs_trans: ∀R. lfeq_transitive R →
32 ∀L1,L,T. L1 ≐[T] L → ∀L2. L ⪤*[R, T] L2 → L1 ⪤*[R, T] L2.
33 /4 width=16 by lfeq_fsle_comp, lfxs_trans_fsle, lfxs_trans_next/ qed-.