[shkkmo]

In a proof, you can absolutely assume something like "A is true", you do it as a part of a sub-proof. Then anything you prove in the sub-proof like "B is true" can be brought back into the main proof in the form: A implies B is true.

The blog post glosses over this assumption and thus ends up concluding "p(n) implies p(n+1)" instead of "p(n) implies (n>1 implies p(n+1))”