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Generalization of the induction principle:

*Proposition:* In order to prove

it suffices to proveforallxinN:F

(forallxinN: (foralln<x:F[x<-n]) =>F).

*Induction Hypothesis*. We take arbitrary`x`in**N**and assume**forall**`n`<`x`:`F`[`x`<-`n`].*Induction Step*: We show`F`.

Author: Wolfgang Schreiner

Last Modification: November 24, 1999