Node case:
 P(t1), P(t2) ==> P(Node t1 t2)
 (N t1) < 2^(H t1), (N t2) < 2^(H t2) ==> (N (Node t1 t2)) < 2^(H (Node t1 t2))
 (N t1) < 2^(H t1), (N t2) < 2^(H t2) ==> (N t1) + (N t2) + 1 < 2^(1 + (max (H t1) (H t2)))

  (N t1) + (N t2) + 1
 { hypothesis P(t1) }
< 2^(H t1) + (N t2) + 1
 { hypothesis P(t2) }
< 2^(H t1) + 2^(H t2) + 1
 { definition of < on integers }
<= 2^(H t1) + 2^(H t2)
 { a < max a b }
<= 2^(max (H t1) (H t2)) + 2^(max (H t1) (H t2))
 { arithmetic }
= 2 * 2^(max (H t1) (H t2))
 { exponentiation }
= 2^(1 + (max (H t1) (H t2)))

so this chain proves: (N t1) + (N t2) + 1 < 2^(1 + (max (H t1) (H t2)))