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We present a fully mechanized proof of correctness and stability of the insertion sort algorithm, while handling stability not as an afterthought in its formal specification, but rather as a property removing any unspecified behaviour from the algorithm, by explaining what happens to elements that are considered equivalent. We therefore express the combined notion of being sorted along with stability as a single inductive predicate, allowing us to share uncovered information in proofs,doi:10.15546/aeei-2018-0015 fatcat:umz3xlpox5gsnn5uax6gmoo3q4