Prove consistency of maximum of two consistent heuristic functions?
Proof (Show consistency property of $h_3$):

$$
h_3(n) = \max(h_1(n), h_2(n)) \\ 
\leq max(h_1(n')+c(n,a,n'), \ h_2(n')+c(n,a,n')) \\ 
\leq \max(h_1(n'), \ h_2(n')) + c(n,a,n') = h_3(n') + c(n,a,n')
$$