Page "learned" Paragraph 1378

For any choice of admissible policy Af in the first stage, the state of the stream leaving this stage is given by Af.

This is the feed state of the subsequent Af stages which, according to the principle of optimality, must use an optimal Af-stage policy with respect to this state.

This will result in a value Af of the objective function, and when Af is chosen correctly this will give Af, the maximum of the objective function.

Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).

The sequence of equations ( 6 ) can be solved for Af when Af is known, and clearly Af, the maximization being over all admissible Af.