X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Fnat_ordered_set.ma;h=d4aa1d57d18780367e650b63dc9ad37eb0109a72;hb=6e2dfd0a82ab76d3c0aeec5f6149e7ee5992d687;hp=d625d391d72934654b9730b33961acbf9f3e0822;hpb=3c1ca5620048ad842144fba291f8bc5f0dca7061;p=helm.git

diff --git a/helm/software/matita/contribs/dama/dama/nat_ordered_set.ma b/helm/software/matita/contribs/dama/dama/nat_ordered_set.ma
index d625d391d..d4aa1d57d 100644
--- a/helm/software/matita/contribs/dama/dama/nat_ordered_set.ma
+++ b/helm/software/matita/contribs/dama/dama/nat_ordered_set.ma
@@ -44,15 +44,18 @@ cases (nat_discriminable x z); [2: left; assumption] cases H1; clear H1;
 qed.
   
 lemma nat_ordered_set : ordered_set.
-apply (mk_ordered_set ? nat_excess);
-[1: intro x; intro; apply (not_le_Sn_n ? H);
-|2: apply nat_excess_cotransitive]
+letin hos ≝ (mk_half_ordered_set nat nat_excess ? nat_excess_cotransitive);[
+  intro x; intro H; apply (not_le_Sn_n ? H);]
+constructor 1;  
+[ apply hos; | apply (dual_hos hos); | reflexivity]
 qed.
 
+interpretation "ordered set N" 'N = nat_ordered_set.
+
 alias id "le" = "cic:/matita/nat/orders/le.ind#xpointer(1/1)".
 lemma os_le_to_nat_le:
   ∀a,b:nat_ordered_set.a ≤ b → le a b.
-intros; normalize in H; apply (not_lt_to_le ?? H);
+intros; normalize in H; apply (not_lt_to_le b a H);
 qed.
  
 lemma nat_le_to_os_le:
@@ -60,6 +63,7 @@ lemma nat_le_to_os_le:
 intros 3; apply (le_to_not_lt a b);assumption;
 qed.
 
+(*
 lemma nat_lt_to_os_lt:
   ∀a,b:nat_ordered_set.a < b → lt nat_ordered_set a b.
 intros 3; split;
@@ -71,4 +75,5 @@ lemma os_lt_to_nat_lt:
   ∀a,b:nat_ordered_set. lt nat_ordered_set a b → a < b.
 intros; cases H; clear H; cases H2;
 [2: apply H;| cases (H1 H)]
-qed.
\ No newline at end of file
+qed.
+*)
\ No newline at end of file