Any example is a base case that is sufficient for starting an inductive truth, as long as it is covered in your inductive rule. The actual error is is a logic

Any example is a base case that is sufficient for starting an inductive truth, as long as it is covered in your inductive rule. The actual error is is a logic error in the proof of the inductive rules that takes a logical step that only holds for n>=2 but doesn't acknowledge that condition. If that logical step is done properly and the condition made explicit, it is clear that a base case of n=1 won't prove anything with that inductive rule that only applies to n>=2.