dynamic programming – How is equation 1 simplified to equation 2 as shown below

In CLRS (Intro to algorithms) on page 362, it says this eqn(1) :eqn 1

can be simplified to this equation(2) :
eqn 2

I would like to know how this simplification was arrived at. It shouldn’t necessarily be a formal proof but one that makes logical and intuitive sense. (General arguments or assumptions that lead to this simplification are also welcomed). Any effort is much appreciated. (Thanks)