More notation here and there: \sup, \divides, \ndivides, !

[helm.git] / helm / matita / library / nat / compare.ma

diff --git a/helm/matita/library/nat/compare.ma b/helm/matita/library/nat/compare.ma
index 194b38d84f255e3924a3273919f01bb96d320ca5..e20d824df5ae105129599fda2b93beac3a23fcfb 100644 (file)
--- a/helm/matita/library/nat/compare.ma
+++ b/helm/matita/library/nat/compare.ma
@@ -14,9 +14,9 @@
 
 set "baseuri" "cic:/matita/nat/compare".
 
-include "nat/orders.ma".
 include "datatypes/bool.ma".
 include "datatypes/compare.ma".
+include "nat/orders.ma".
 
 let rec eqb n m \def 
 match n with 
@@ -43,7 +43,7 @@ simplify.reflexivity.
 simplify.apply not_eq_O_S.
 intro.
 simplify.
-intro. apply not_eq_O_S n1 ?.apply sym_eq.assumption.
+intro. apply not_eq_O_S n1.apply sym_eq.assumption.
 intros.simplify.
 generalize in match H.
 elim (eqb n1 m1).
@@ -89,7 +89,7 @@ simplify.intros.apply H.apply le_S_S_to_le.assumption.
 qed.
 
 theorem leb_elim: \forall n,m:nat. \forall P:bool \to Prop. 
-(n \leq m \to (P true)) \to (\not (n \leq m) \to (P false)) \to
+(n \leq m \to (P true)) \to (\lnot (n \leq m) \to (P false)) \to
 P (leb n m).
 intros.
 cut 
@@ -154,8 +154,8 @@ simplify.apply le_S_S.apply le_O_n.
 intro.simplify.apply le_S_S. apply le_O_n.
 intros 2.simplify.elim (nat_compare n1 m1).
 simplify. apply le_S_S.apply H.
-simplify. apply le_S_S.apply H.
 simplify. apply eq_f. apply H.
+simplify. apply le_S_S.apply H.
 qed.
 
 theorem nat_compare_n_m_m_n: \forall n,m:nat. 
@@ -181,6 +181,6 @@ cut match (nat_compare n m) with
 apply Hcut.apply nat_compare_to_Prop.
 elim (nat_compare n m).
 apply (H H3).
-apply (H2 H3).
 apply (H1 H3).
+apply (H2 H3).
 qed.