Please, I really need correct answer!!! Problem $6(10\%)$ Starting from an empty Fibonacci heap and performing INS, MIN, and Extract$\_$MIN

operations multiple times $($in arbitrary order$),$ is it always true that, in the final heap structure, every tree

with root degree r must have exactly $2^($r$)$ nodes, and there is at most one tree with root degree r for every

r $>=1?$ You must either formally prove the correctness or find a counterexample and briefly explain.