Definition 2.1. Suppose f is a k-place function (k ≥ 1) and
g is a (k + 2)-place function. The function defined by primitive recursion from f and g is the (k + 1)-place function h defined by the equations
h(x0, . . . , xk−1,y) = f (x0, . . . , xk−1)
h(x0, . . . , xk−1,y + 1) = g (x0, . . . , xk−1,y,h(x0, . . . , xk−1,y))
Proposition 2.5. The multiplication function
mult(x,y) = x · y is primitive recursive.
Problem : Prove Proposition 2.5 by showing that the primitive recursive definition of mult is can be put into the form re-quired by Definition 2.1 and showing that the corresponding functions f and g are primitive recursive.