It can be handy to think about consistency in terms of an invariant - in these situations the invariant is "this data structure is consistent/valid", and you need to prove to yourself that the code preserves that invariant at every point, no matter what happens. An easy way to do this to divide up your code into atomic "steps", and to prove that each step preserves the invariant on its own. Then you can conclude that the invariant will hold no matter which steps run or the order that they run in.
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