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Complete Induction

Generalization of the induction principle:

Proposition: In order to prove

forall x in N: F
it suffices to prove
(forall x in N: (forall n < x: F[x <- n]) => F).
  1. Induction Hypothesis. We take arbitrary x in N and assume
    forall n < x: F[x <- n].
  2. Induction Step: We show F.

Author: Wolfgang Schreiner
Last Modification: November 24, 1999

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