symmetry of inequality sym_neq

diff --git a/helm/software/matita/library/logic/equality.ma b/helm/software/matita/library/logic/equality.ma
index 6e38ae71e80087feea60c5f27d91f21ffa6361e1..f4f12ec6c103a8290765517c95b151985e04cbab 100644 (file)
--- a/helm/software/matita/library/logic/equality.ma
+++ b/helm/software/matita/library/logic/equality.ma
@@ -48,6 +48,13 @@ qed.
 variant trans_eq : \forall A:Type.\forall x,y,z:A. x=y  \to y=z \to x=z
 \def transitive_eq.
 
+theorem symmetric_not_eq: \forall A:Type. symmetric A (λx,y.x ≠ y).
+unfold symmetric.simplify.intros.unfold.intro.apply H.apply sym_eq.assumption.
+qed.
+
+variant sym_neq: ∀A:Type.∀x,y.x ≠ y →y ≠ x
+≝ symmetric_not_eq.
+
 theorem eq_elim_r:
  \forall A:Type.\forall x:A. \forall P: A \to Prop.
    P x \to \forall y:A. y=x \to P y.