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 "static_2/syntax/sh_lt.ma".
16 include "static_2/syntax/sd_d.ma".
18 (* SORT DEGREE **************************************************************)
20 (* Properties with sh_lt ****************************************************)
22 lemma deg_SO_gt (h): sh_lt h →
23 ∀s1,s2. s1 < s2 → deg_SO h s1 s2 0.
24 #h #Hh #s1 #s2 #Hs12 @deg_SO_zero * normalize
26 elim (nlt_inv_refl … Hs12)
28 lapply (next_lt … Hh ((pr_next h)^n s2)) >H -H #H
29 lapply (nlt_trans … H Hs12) -s1 #H1
30 /3 width=5 by nlt_ge_false, nexts_le/ (* full auto too slow *)