Subtract values in hash from corresponding values in another hash

I'd like to be able to subtract two hashes and get a third hash in Ruby.

The two hashes look like this:

h1 = {"Cat" => 100, "Dog" => 5, "Bird" => 2, "Snake" => 10}
h1.default = 0

h2 = {"cat" => 50, "dog" => 3, "BIRD" => 4, "Mouse" => 75, "Snake" => 10}
h2.default = 0

I'd like to be able to call a method on h1 like this:

h1.difference(h2)

and get this hash as a result:

{"Cat" => 50, "Dog" => 2, "BIRD" => -2, "Mouse" => -75}

I'd like to create a new hash with keys from both Hashes and the values of the new hash to be the value of the key in the first hash minus the value of that key in the second hash. The catch is that I'd like this Hash method to work regardless of the case of the keys. In other words, I'd like "Cat" to match up with "cat".

Here's what I have so far:

class Hash
  def difference(another_hash)
    (keys + another_hash.keys).map { |key| key.strip }.uniq.inject(Hash.new(0)) { |acc, key| acc[key] = (self[key] - another_hash[key]); acc }.delete_if { |key, value| value == 0 }
  end
end

This is OK, but, unfortunately, the result isn't what I want.

Any help would be appreciated.