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(**) Symmetric binary trees

Let us call a binary tree symmetric if you can draw a vertical line through the root node and then the right subtree is the mirror image of the left subtree. Write a predicate symmetric/1 to check whether a given binary tree is symmetric. Hint: Write a predicate mirror/2 first to check whether one tree is the mirror image of another. We are only interested in the structure, not in the contents of the nodes.

mirror Empty          Empty          = True
mirror (Branch _ a b) (Branch _ x y) = mirror a y && mirror b x
mirror _              _              = False
 
symmetric Empty          = True
symmetric (Branch _ l r) = mirror l r