#A: A function φ definable explicitly from functions Ψ and constants q₁, ... q_n is primitive recursive in Ψ.

#B: The finite sum Σ_y<z ψ(x, y) and product Π_y<zψ(x, y) are primitive recursive in ψ.

#C: A predicate P obtained by substituting functions χ₁,..., χ_m for the respective variables of a predicate Q is primitive recursive in χ₁,..., χ_m, Q.

#D: The following predicates are primitive recursive in Q and R: