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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/notation/relations/lazyeqsn_3.ma".
16 include "basic_2/static/lfxs.ma".
18 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
20 (* Basic_2A1: was: lleq *)
21 definition lfeq: relation3 term lenv lenv ≝
25 "syntactic equivalence on referred entries (local environment)"
26 'LazyEqSn T L1 L2 = (lfeq T L1 L2).
28 (* Basic_2A1: uses: lleq_transitive *)
29 definition lfeq_transitive: predicate (relation3 lenv term term) ≝
30 λR. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≡[T1] L2 → R L1 T1 T2.
32 (* Basic_properties *********************************************************)
34 lemma lfxs_transitive_lfeq: ∀R. lfxs_transitive ceq R R → lfeq_transitive R.
37 (* Basic inversion lemmas ***************************************************)
39 lemma lfeq_transitive_inv_lfxs: ∀R. lfeq_transitive R → lfxs_transitive ceq R R.
42 (* Basic forward lemmas *****************************************************)
44 (* Basic_2A1: was: llpx_sn_lrefl *)
45 (* Note: this should have been lleq_fwd_llpx_sn *)
46 lemma lfeq_fwd_lfxs: ∀R. c_reflexive … R →
47 ∀L1,L2,T. L1 ≡[T] L2 → L1 ⪤*[R, T] L2.
48 #R #HR #L1 #L2 #T * #f #Hf #HL12
49 /4 width=7 by lexs_co, cext2_co, ex2_intro/
52 (* Basic_2A1: removed theorems 10:
53 lleq_ind lleq_fwd_lref
54 lleq_fwd_drop_sn lleq_fwd_drop_dx
55 lleq_skip lleq_lref lleq_free
56 lleq_Y lleq_ge_up lleq_ge