Go backward to Induction over Multiple ArgumentsGo up to TopGo forward to Inductively Defined Predicate |

*Definition:* An
*inductive definition* over **N**
of an `n`-ary predicate `p`:

p(x_{0}, ..., 0, ...,x_{n-1}): <=> F_{b},p(x_{0}, ...,x_{i}+1, ...,x_{n-1}): <=> F_{r}

`p`does not occur in*base formula*`F`_{b}.- Every application of
`p`in*recursion formula*`F`_{r}has form`p`(`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