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so last time around we looked to see how induction can be used not just as a proof technique but also as a technique for constructing programs and we Illustrated this by means of an example we saw how the idea of so-called constructive induction could be used to obtain a fast version of the standard function which reverses a list so what weamp;#39;re going to do today is weamp;#39;re going to kick things off with a quick review of what we did last time around and then weamp;#39;re going to be doing two things first of all weamp;#39;re going to be doing a second example of constructive induction weamp;#39;ll be seeing how it can be used to obtain a fast version of a function which flattens a tree and then secondly weamp;#39;re going to be looking at the final case study which weamp;#39;re going to have in the course which is a compiler correctness result so here is a quick summary of what we achieved in the last lecture so what we have in the top red box is the standard recursive