updating the structures for sorts

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / sd_lt.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma
new file mode 100644 (file)
index 0000000..238d1a2
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+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "static_2/syntax/sh_lt.ma".
+include "static_2/syntax/sd_d.ma".
+
+(* SORT DEGREE **************************************************************)
+
+(* Properties with sh_lt ****************************************************)
+
+lemma deg_SO_gt (h): sh_lt h →
+      ∀s1,s2. s1 < s2 → deg_SO h s1 s2 0.
+#h #Hh #s1 #s2 #Hs12 @deg_SO_zero * normalize
+[ #H destruct
+  elim (lt_refl_false … Hs12)
+| #n #H
+  lapply (next_lt … Hh ((next h)^n s2)) >H -H #H
+  lapply (transitive_lt … H Hs12) -s1 #H1
+  /3 width=5 by lt_le_false, nexts_le/ (* full auto too slow *)
+]
+qed.