Natural numbers/Proofs/Induction principle/Fact/Proof2

Proof

Due to the first condition, ${}A(0)$ holds. Due to the second condition, we get that also ${}A(1)$ holds. Therefore also ${}A(2)$ holds. Therefore also ${}A(3)$ holds. Because we can move on step by step and reach every natural number, we conclude that the statement ${}A(n)$ holds for every natural number ${}n$

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