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 *)
13 (**************************************************************************)
15 include "basic_2/rt_computation/fsb_aaa.ma".
16 include "basic_2/dynamic/cnv_aaa.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Forward lemmas with strongly rst-normalizing closures ********************)
22 (* Note: this is the "big tree" theorem *)
23 (* Basic_2A1: uses: snv_fwd_fsb *)
24 lemma cnv_fwd_fsb (h) (a):
25 ∀G,L,T. ❨G,L❩ ⊢ T ![h,a] → ≥𝐒 ❨G,L,T❩.
26 #h #a #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
29 (* Forward lemmas with strongly rt-normalizing terms ************************)
31 lemma cnv_fwd_csx (h) (a):
32 ∀G,L,T. ❨G,L❩ ⊢ T ![h,a] → ❨G,L❩ ⊢ ⬈*𝐒 T.
34 /3 width=3 by cnv_fwd_fsb, fsb_inv_csx/
37 (* Inversion lemmas with proper parallel rst-computation for closures *******)
39 lemma cnv_fpbg_refl_false (h) (a):
40 ∀G,L,T. ❨G,L❩ ⊢ T ![h,a] → ❨G,L,T❩ > ❨G,L,T❩ → ⊥.
41 /3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.