Can I evict for this rule being broken in the lease?

[Tim Callahan]

Hi, we have a lease that allows dogs as long as they are on a leash at all times when the dog is outside and on the property.  This is specifically stated in the lease.  It's a safely issue for us, as we live in another unit in the house.  Now I have a tenant who has broken this rule several times, letting their small dog run free everywhere. It ran after a car coming up the driveway the other day and was barking at our guests. 

We have posted warning letters on their door twice now about this.

How would we fare if we started eviction proceedings because the tenant refuses to obey this rule?