More notation here and there.

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

diff --git a/helm/matita/library/nat/orders.ma b/helm/matita/library/nat/orders.ma
index 71cd5945037fe43fe3d9dbdef3a8ae5fd5770186..796567fa59ae31483de19312a03f49520b73e96c 100644 (file)
--- a/helm/matita/library/nat/orders.ma
+++ b/helm/matita/library/nat/orders.ma
@@ -104,11 +104,11 @@ intros.elim H.exact I.exact I.
 qed.
 
 (* not le *)
-theorem not_le_Sn_O: \forall n:nat. \lnot (S n \leq O).
+theorem not_le_Sn_O: \forall n:nat. S n \nleq O.
 intros.simplify.intros.apply leS_to_not_zero ? ? H.
 qed.
 
-theorem not_le_Sn_n: \forall n:nat. \lnot (S n \leq n).
+theorem not_le_Sn_n: \forall n:nat. S n \nleq n.
 intros.elim n.apply not_le_Sn_O.simplify.intros.cut S n1 \leq n1.
 apply H.assumption.
 apply le_S_S_to_le.assumption.
@@ -123,7 +123,7 @@ left.simplify.apply le_S_S.assumption.
 qed.
 
 (* not eq *)
-theorem lt_to_not_eq : \forall n,m:nat. n<m \to \lnot (n=m).
+theorem lt_to_not_eq : \forall n,m:nat. n<m \to n \neq m.
 simplify.intros.cut (le (S n) m) \to False.
 apply Hcut.assumption.rewrite < H1.
 apply not_le_Sn_n.
@@ -141,16 +141,16 @@ simplify.intros.
 apply le_S_S_to_le.assumption.
 qed.
 
-theorem not_le_to_lt: \forall n,m:nat. \lnot (n \leq m) \to m<n.
+theorem not_le_to_lt: \forall n,m:nat. n \nleq m \to m<n.
 intros 2.
-apply nat_elim2 (\lambda n,m.\lnot (n \leq m) \to m<n).
+apply nat_elim2 (\lambda n,m.n \nleq m \to m<n).
 intros.apply absurd (O \leq n1).apply le_O_n.assumption.
 simplify.intros.apply le_S_S.apply le_O_n.
 simplify.intros.apply le_S_S.apply H.intros.apply H1.apply le_S_S.
 assumption.
 qed.
 
-theorem lt_to_not_le: \forall n,m:nat. n<m \to \lnot (m \leq n).
+theorem lt_to_not_le: \forall n,m:nat. n<m \to m \nleq n.
 simplify.intros 3.elim H.
 apply not_le_Sn_n n H1.
 apply H2.apply lt_to_le. apply H3.