Describe the goods in the circular flow, Macroeconomics

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Goods in the circular flow

If Y_R is total value of all goods going from F_R to F_H, then total value added from all firms in the F_R box is equal to Y_R(they don't purchase any goods to which they add value).
In the similar way, if total value of all goods going from F_H to F_F is given by Y_H, then total value added from all firms in the F_H box is Y_H- Y_R.
In the similar way, total value added for all firms in FF box would be equal to Y- Y_H. If we sum all the value added from all firms, we get Y_R+ (Y_H- Y_R) + (Y- Y_H) = Y.
This result is independent of how many "levels" or boxes we have in production process. Rather than 3 levels, we could have any number of levels and result would still hold. Additionally, a particular firm may be producing in numerous of the boxes.

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