I'm trying to solve the following question as part of my preparations for the final the "Advance Algorithms" course:
Let's look at a minimum stack that consists of a single tree, with the root of the tree having degree $\deg(r)=7$. Determined. Prove or disprove the following state in a Fibonacci heap: All children of the root have degrees in the value range $\deg(u)\in\{0,1,2,4\}$. If the situation is possible - briefly present a series of actions that lead to it. If the situation is not possible - present a direct and accurate proof of this.
In the answer they stated that this situation is not possible. But how do you actually formally prove it? Do I need to look at the previous state? How can I know how it would look like?