I have a doubt about the induction principle. Let's prove that $p(n)$ is true $\forall n\geq n_0$.
The first step consists in verifying that: $p(n_0)$ is true.
The inductive step consists in supposing that $p(n)$ is true and proving that $p(n+1)$ is too.
Doubt: if I say that $p(n)$ is true (inductive hypothesis) than can I say that $p(n-1),p(n-2),...$ are true?