repeat'
  first
  | apply Even.add_two
  | apply Even.zero
case left

⊢ Even 4

case right.left

⊢ Even 7

case right.right.left

⊢ Even 3

case right.right.right

⊢ Even 0
case right.left.a.a.a

⊢ Even 1

case right.right.left.a

⊢ Even 1