feat: Adding proofs of correctness and time complexity of insertion sort #280
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I have added the file
InsertionSort.leanin this PR. I am aware thatList.insertionSortexists, but it is not instrumented withtick, which does not make it possible to write the complexity proof. I have chosen the worst case time bound asn^2but the same proof discharges forn(n+1)/2. I know I have not added the required documentation in this PR, but I first want to get an OK for the actual proofs implemented.I think insertion sort, while a very simple algorithm, merits its inclusion because more complicated sorts implemented in the standard libraries of programming languages (like "TimSort" in Python) use insertion sort to quickly sort smaller sub-arrays as insertion sort is faster than divide-and-conquer based comparison sorts like merge and quick sort for very small arrays. I believe that the proofs in this file would aid future proofs about these hybrid in-actual-use sorts.