Simple Proofs of the Summation and Connectivity Theorems in Metabolic Control Analysis

In the early 1970s, the Kacser/Burns and the Heinrich/Rapoport groups independently discovered the important summation and connectivity theorems in metabolic control analysis. These theorems were derived originally by using thought experiments and proved mathematically later. The mathematical proofs are not easy for me to read and follow. But the proofs actually can be very simple and need only a couple of lines as I give here.