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Structural Induction

Proposition: In order to prove a property

forall x in S: F
for an inductively defined set S, it suffices to prove
forall x1,...,xmi, y1 in S, ..., yni in S:
   (F[x := y1] /\  ... /\  F[x := yni]) =>
      F[x := fi(x1,...,xmi, y1, ..., yni)]
for every constructor fi of S.
Author: Wolfgang Schreiner
Last Modification: November 24, 1999

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