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I find this picture proof just as persuasive as a proof by mathematical induction.

As far as investigating AA/NA, I know by the the principle of mathematical induction that if you can show you can get to the first step and for all arbitrary values, k, by the rule of implication if you can get to step k and you prove you can get to step k+1 with the inductive hypothesis, then you can reach all the steps in the program.

Therefore, the program is sound by the principle of mathematical induction.

If loop invariants remind you of mathematical induction, they should. 

This is the principle of what is called “mathematical induction.”