NO Pets Policy Scenario- tenant has a doctors note to have a dog. Other tenant gives doctors note of severe pet alergies. who wins?

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Question: 

With a no pets policy, tenant brings a doctors note stating she medically prescribed to have a service dog to counteract anxiety condition, she moved in without a pet and knew the policy beforehand. 

Other Tenant in the property has a past doctors description of their severe allergic reaction to pets( hence why they moved into a no pets policy building). 

who wins? Can you write in the lease a statement to address tenants trying to get around the no pets policy with doctors notes?