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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 "basic_2/static/lfxs_fqup.ma".
16 include "basic_2/static/lfdeq.ma".
18 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
20 (* Advanced properties ******************************************************)
22 (* Basic_2A1: uses: lleq_refl *)
23 lemma lfdeq_refl: ∀h,o,T. reflexive … (lfdeq h o T).
24 /2 width=1 by lfxs_refl/ qed.
26 lemma lfdeq_pair: ∀h,o,V1,V2. V1 ≡[h, o] V2 →
27 ∀I,L. ∀T:term. L.ⓑ{I}V1 ≡[h, o, T] L.ⓑ{I}V2.
28 /2 width=1 by lfxs_pair/ qed.
30 (* Advanced inversion lemmas ************************************************)
32 lemma lfdeq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. L1 ≡[h, o, ⓑ{p,I}V.T] L2 →
33 L1 ≡[h, o, V] L2 ∧ L1.ⓧ ≡[h, o, T] L2.ⓧ.
34 /2 width=3 by lfxs_inv_bind_void/ qed-.
36 (* Advanced forward lemmas **************************************************)
38 lemma lfdeq_fwd_bind_dx_void: ∀h,o,p,I,L1,L2,V,T.
39 L1 ≡[h, o, ⓑ{p,I}V.T] L2 → L1.ⓧ ≡[h, o, T] L2.ⓧ.
40 /2 width=4 by lfxs_fwd_bind_dx_void/ qed-.