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The assumption that the statement holds for some arbitrary case $k$.

A detailed verification that the base case meets the condition of the theorem or statement being proved.

Show that the statement holds for the first natural number, usually 0 or 1.

The choice of initial value for which the basis step establishes the truth of the statement.

Prove the statement for the base cases, which may include several initial natural numbers, not just the first.

Show that each case follows from the previous one, or from the collection of all previous ones in strong induction.

State that, since the basis step and inductive step have been proved, by induction the statement is true for all natural numbers.

Assume the statement holds for some arbitrary natural number $k$ and show it holds for $k+1$.

Arriving at the end of the induction process, concluding the statement holds for all natural numbers.