# Checking if two inequalities are equivalent

I ask:

```
var("x y")
assume(x,'integer')
assume(y,'integer')
print (x>y)==(y<x)
print (x>y)==(x-y>0)
```

and get:

```
True
False
```

So Sage recognizes the equivalence in the first pair but not in the second pair. Is there a way to handle this?

Maybe rather use the Polyhedron class. Symbolic ring is a big mess.