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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 *)
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/rdeq_fqup.ma".
16 include "basic_2/rt_computation/rdsx.ma".
18 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
20 (* Advanced properties ******************************************************)
22 (* Basic_2A1: uses: lsx_atom *)
23 lemma lfsx_atom (h) (o) (G) (T): G ā¢ ā¬*[h, o, T] šā¦āā¦.
25 @rdsx_intro #Y #H #HnT
26 lapply (lpx_inv_atom_sn ā¦ H) -H #H destruct
30 (* Advanced forward lemmas **************************************************)
32 (* Basic_2A1: uses: lsx_fwd_bind_dx *)
33 (* Note: the exclusion binder (ā§) makes this more elegant and much simpler *)
34 (* Note: the old proof without the exclusion binder requires lreq *)
35 lemma rdsx_fwd_bind_dx (h) (o) (G):
36 āp,I,L,V,T. G ā¢ ā¬*[h, o, ā{p,I}V.T] šā¦Lā¦ ā
37 G ā¢ ā¬*[h, o, T] šā¦L.ā§ā¦.
38 #h #o #G #p #I #L #V #T #H
39 @(rdsx_ind ā¦ H) -L #L1 #_ #IH
41 elim (lpx_inv_unit_sn ā¦ H) -H #L2 #HL12 #H destruct
42 /4 width=4 by rdeq_fwd_bind_dx_void/
45 (* Advanced inversion lemmas ************************************************)
47 (* Basic_2A1: uses: lsx_inv_bind *)
48 lemma rdsx_inv_bind (h) (o) (G): āp,I,L,V,T. G ā¢ ā¬*[h, o, ā{p,I}V.T] šā¦Lā¦ ā
49 ā§ā§ G ā¢ ā¬*[h, o, V] šā¦Lā¦ & G ā¢ ā¬*[h, o, T] šā¦L.ā§ā¦.
50 /3 width=4 by rdsx_fwd_pair_sn, rdsx_fwd_bind_dx, conj/ qed-.