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Mathematical Induction

Third Peano Axiom:

(F[x <- 0] /\  (forall x in N: F => F[x <- x+1])) => forall x in N: F.

Proposition: In order to prove

forall x in N: F,

1. F[x <- 0],
2. (forall x in N: F => F[x <- x+1]).