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Inductive Function Definitions

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

f(x0, ..., 0, ..., xn-1)	:=	Tb,
f(x0, ..., xi+1, ..., xn-1)	:=	Tr

• f does not occur in base term T_b.
• Every application of f in  recursion term T_r has form

  f(T₀, ..., x_i, ..., T_n-1)

• Free variables of terms must occur in definiendum.

Induction runs over x_i.