X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2FZ%2Fplus.ma;fp=helm%2Fsoftware%2Fmatita%2Flibrary%2FZ%2Fplus.ma;h=cd565124589d1e20dbac077a384e1aac6fa06125;hb=f262223fb7b49a191b25d27ecc58818b9d7a357d;hp=2b439b92e273c83d0e9175bd402d32d0fb363b64;hpb=0ca6c1688d9000997977e6b1bad9a8c997c81d08;p=helm.git

diff --git a/helm/software/matita/library/Z/plus.ma b/helm/software/matita/library/Z/plus.ma
index 2b439b92e..cd5651245 100644
--- a/helm/software/matita/library/Z/plus.ma
+++ b/helm/software/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.
@@ -299,6 +303,26 @@ 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).