Composition is the only independent rule in Kleene's model of partial recursive functions

The following two theorems:

Theorem 1: The primitive recursive rule is reducible to repeated applications of specific compositions.
Theorem 2: The minimization (least-search) rule is reducible to repeated applications of specific compositions.

led to:

Corollary: Any computation defined by Kleene's model of partial recursive functions can be done, according to Theorem 1 and Theorem 2, using the initial functions and the repeated application of the composition rule.

The profs can be found in [1].

References