The recursive data type, binary-2PTG. of binary trees with leaf labels, L, is de

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The recursive data type, binary-2PTG. of binary trees with leaf labels, L, is defined recursively as follows: defined recursively on this definition by: | (bintree. GX. G2) = |G1| + |G2| + 1- For example, the size of the binary-2PTG. G, pictured in Write out (using angle brackets and labels bintree, leaf, etc. ) the binary-2PTG. G, pictured in Figure 6. 1. The value of flatten(G) for is the sequence of labels in L of the leaves of G. For example, for the binary-2PTG. G, pictured in Figure 6. 1, flatten(G) = (win, lose, win, win). Give a recursive definition of flatten. (You may use the operation of concatenation (append) of two sequences. ) Prove by structural induction on the definitions of flatten and size that 2 length(flatten(G)) = |G| + 1.

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