Argue the correctness of BINOMIAL-HEAP-UNION using the following loop invariant:
At the start of each iteration of the while loop of lines 9–21, x points to a root that is one of the following:
• the only root of its degree,
• the first of the only two roots of its degree, or
• the first or second of the only three roots of its degree.
Moreover, all roots preceding x’s predecessor on the root list have unique degrees on the root list, and if x’s predecessor has a degree different from that of x, its degree on the root list is unique, too. Finally, node degrees monotonically increase as we traverse the root list.
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