1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "static_2/static/rex_fqup.ma".
16 include "static_2/static/rdeq.ma".
18 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
20 (* Advanced properties ******************************************************)
22 lemma rdeq_refl: ∀h,o,T. reflexive … (rdeq h o T).
23 /2 width=1 by rex_refl/ qed.
25 lemma rdeq_pair_refl: ∀h,o,V1,V2. V1 ≛[h, o] V2 →
26 ∀I,L. ∀T:term. L.ⓑ{I}V1 ≛[h, o, T] L.ⓑ{I}V2.
27 /2 width=1 by rex_pair_refl/ qed.
29 (* Advanced inversion lemmas ************************************************)
31 lemma rdeq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. L1 ≛[h, o, ⓑ{p,I}V.T] L2 →
32 L1 ≛[h, o, V] L2 ∧ L1.ⓧ ≛[h, o, T] L2.ⓧ.
33 /2 width=3 by rex_inv_bind_void/ qed-.
35 (* Advanced forward lemmas **************************************************)
37 lemma rdeq_fwd_bind_dx_void: ∀h,o,p,I,L1,L2,V,T.
38 L1 ≛[h, o, ⓑ{p,I}V.T] L2 → L1.ⓧ ≛[h, o, T] L2.ⓧ.
39 /2 width=4 by rex_fwd_bind_dx_void/ qed-.