* The case ''firstn'' case = 1 is [[vacuous truth|vacuously true]];
* the step that goes fromproves the case ''n''th = k + 1 caseis totrivial, but relies on '''two''' previous cases: the (case ''n'' += 1)th''k'' caseand isthe trivial ifcase ''n'' =&genbsp;2. This step cannot be used to prove the the case ''n'' = 2 andas impossibleto ifdo so would be a [[circular argument]] (since the case ''n'' = 1 2 had not yet been proved).
* the substantial part of the proof is to give a (different) proof of the case ''second casen''; = 2.
* the second case is relied on in the trivial induction step.
