X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Fsh.ma;h=bab748f7564ff60dfcab989f7cacc04ec7369abf;hb=ab0d181f9a89f461a9c280f42a949a2dc2abe44c;hp=7c31b884fedb8af6f7522c481210030ab34bd521;hpb=2368e490e9b948097cee58ae7c9d4915d1c3746f;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma b/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
index 7c31b884f..bab748f75 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/arith.ma".
+include "ground_2/lib/arith.ma".
 
 (* SORT HIERARCHY ***********************************************************)
 
@@ -33,7 +33,12 @@ lapply (next_lt h ((next h)^l k)) #H
 lapply (le_to_lt_to_lt … IHl H) -IHl -H /2 width=2/
 qed.
 
+lemma nexts_lt: ∀h,k,l. k < (next h)^(l+1) k.
+#h #k #l >iter_SO
+lapply (nexts_le h k l) #H
+@(le_to_lt_to_lt … H) //
+qed.
+
 axiom nexts_dec: ∀h,k1,k2. Decidable (∃l. (next h)^l k1 = k2).
 
 axiom nexts_inj: ∀h,k,l1,l2. (next h)^l1 k = (next h)^l2 k → l1 = l2.
-