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Proposition: Let T be a tree of height h where every node has an outdegree of at most 2. The number of tree nodes is less than 2h+1:
forall T: (T is tree /\ forall x in V: outdeg(x) <= 2) => |V| < 2h+1 where V = T0, h = height(T).
Proof: Let T be a such a tree. We proceed by complete induction on the height of T.
|V| <= 1+(2h-1)+(2h-1) = 2h+1-1 < 2h+1.