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/reqx_fqup.ma".
16 include "basic_2/rt_computation/rsx.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) (G) (T): G ⊢ ⬈*𝐒[h,T] ⋆.
26 lapply (lpx_inv_atom_sn … H) -H #H destruct
30 (* Advanced forward lemmas **************************************************)
32 (* Basic_2A1: uses: lsx_fwd_bind_dx *)
33 (* Note: the exclusion binder (ⓧ) makes this more elegant and much simpler *)
34 (* Note: the old proof without the exclusion binder requires lreq *)
35 lemma rsx_fwd_bind_dx_void (h) (G):
36 ∀p,I,L,V,T. G ⊢ ⬈*𝐒[h,ⓑ[p,I]V.T] L → G ⊢ ⬈*𝐒[h,T] L.ⓧ.
37 #h #G #p #I #L #V #T #H
38 @(rsx_ind … H) -L #L1 #_ #IH
40 elim (lpx_inv_unit_sn … H) -H #L2 #HL12 #H destruct
41 /4 width=4 by reqx_fwd_bind_dx_void/
44 (* Advanced inversion lemmas ************************************************)
46 (* Basic_2A1: uses: lsx_inv_bind *)
47 lemma rsx_inv_bind_void (h) (G):
48 ∀p,I,L,V,T. G ⊢ ⬈*𝐒[h,ⓑ[p,I]V.T] L →
49 ∧∧ G ⊢ ⬈*𝐒[h,V] L & G ⊢ ⬈*𝐒[h,T] L.ⓧ.
50 /3 width=4 by rsx_fwd_pair_sn, rsx_fwd_bind_dx_void, conj/ qed-.