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*Definition:* An
*inductive definition* over **N**
of an `n`-ary function `f`:

f(x_{0}, ..., 0, ...,x_{n-1}):= T_{b},f(x_{0}, ...,x_{i}+1, ...,x_{n-1}):= T_{r}

`f`does not occur in*base term*`T`_{b}.- Every application of
`f`in*recursion term*`T`_{r}has form`f`(`T`_{0}, ...,`x`_{i}, ...,`T`_{n-1}) - Free variables of terms must occur in definiendum.

*Induction runs over x_{i}.*

Author: Wolfgang Schreiner

Last Modification: November 24, 1999