- grafiteParser: we added the comand "defined" as a presentational

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / sh.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma b/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
index 7c31b884fedb8af6f7522c481210030ab34bd521..0d09320cc871665e968a39e15b0f3434c31d917a 100644 (file)
--- 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 ***********************************************************)
 
@@ -23,17 +23,22 @@ record sh: Type[0] ≝ {
 }.
 
 definition sh_N: sh ≝ mk_sh S ….
-// qed.
+// defined.
 
 (* Basic properties *********************************************************)
 
 lemma nexts_le: ∀h,k,l. k ≤ (next h)^l k.
 #h #k #l elim l -l // normalize #l #IHl
 lapply (next_lt h ((next h)^l k)) #H
-lapply (le_to_lt_to_lt … IHl H) -IHl -H /2 width=2/
+lapply (le_to_lt_to_lt … IHl H) -IHl -H /2 width=2 by lt_to_le/
+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.
-