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Inductive Predicate Definitions

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

p(x0, ..., 0, ..., xn-1)	: <=>	Fb,
p(x0, ..., xi+1, ..., xn-1)	: <=>	Fr

• p does not occur in base formula F_b.
• Every application of p in  recursion formula F_r has form

  p(T₀, ..., x_i, ..., T_n-1)

• Free variables of terms must occur in definiendum.

Induction runs over x_i.