Induction proof

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This page explains how to prove with induction method on the natural number with Rodin tools. In other words, how to prove :


\forall i.i \in \mathbb{N}\land P(i) \Rightarrow P(i+1)

\forall i. i \in \mathbb{N}  \Rightarrow P(i)

The proof key is the following theorem:

\forall s.s \subseteq \mathbb{N} \land 0 \in s \land  (\forall n.n \in s \Rightarrow n+1 \in s)\Rightarrow  \mathbb{N} \subseteq s

The proof of the previous theorem is given by instantiating the key theorem with : 	  \{x|x\in \mathbb{N} \land P(x)\}