X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2FZ%2Fplus.ma;h=cd565124589d1e20dbac077a384e1aac6fa06125;hb=9e028235daa0abea353d06b4226d4c6698ede3d4;hp=976f6cfb3ce01d379244fc66ec964a99563917d3;hpb=7f2444c2670cadafddd8785b687ef312158376b0;p=helm.git

diff --git a/matita/library/Z/plus.ma b/matita/library/Z/plus.ma
index 976f6cfb3..cd5651245 100644
--- a/matita/library/Z/plus.ma
+++ b/matita/library/Z/plus.ma
@@ -261,6 +261,10 @@ definition Zopp : Z \to Z \def
 (*CSC: the URI must disappear: there is a bug now *)
 interpretation "integer unary minus" 'uminus x = (cic:/matita/Z/plus/Zopp.con x).
 
+theorem eq_OZ_Zopp_OZ : OZ = (- OZ).
+reflexivity.
+qed.
+
 theorem Zopp_Zplus: \forall x,y:Z. -(x+y) = -x + -y.
 intros.
 elim x.elim y.
@@ -299,3 +303,27 @@ rewrite > nat_compare_n_n.
 simplify.apply refl_eq.
 qed.
 
+theorem injective_Zplus_l: \forall x:Z.injective Z Z (\lambda y.y+x).
+intro.simplify.intros (z y).
+rewrite < Zplus_z_OZ.
+rewrite < (Zplus_z_OZ y).
+rewrite < (Zplus_Zopp x).
+rewrite < (Zplus_Zopp x).
+rewrite < assoc_Zplus.
+rewrite < assoc_Zplus.
+apply eq_f2
+  [assumption|reflexivity]
+qed.
+
+theorem injective_Zplus_r: \forall x:Z.injective Z Z (\lambda y.x+y).
+intro.simplify.intros (z y).
+apply (injective_Zplus_l x).
+rewrite < sym_Zplus.
+rewrite > H.
+apply sym_Zplus.
+qed.
+
+(* minus *)
+definition Zminus : Z \to Z \to Z \def \lambda x,y:Z. x + (-y).
+
+interpretation "integer minus" 'minus x y = (cic:/matita/Z/plus/Zminus.con x y).