From 8229ea52c14c52122d92b0aad30131152745552b Mon Sep 17 00:00:00 2001
From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Fri, 8 May 2009 14:39:54 +0000
Subject: [PATCH] symmetry of inequality sym_neq

---
 helm/software/matita/library/logic/equality.ma | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/helm/software/matita/library/logic/equality.ma b/helm/software/matita/library/logic/equality.ma
index 6e38ae71e..f4f12ec6c 100644
--- 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.
-- 
2.39.2