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You are right, I forgot to state an assumption, which is that "a gets pushed out of A" happens before "b gets pushed out of B" (and then goes on to apply to A).

One of those things must happen before the other (each step in the algorithm is a currently-unassigned student applying to their next choice). In your case, if a is the most-preferred non-accepted student for A, then b must have been pushed out of B first, so the argument applies to B instead.



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