The cone theorem states that for the given reaction mechanism and given positive equilibrium, the velocity ("dN/dt") at a state "N" for a system with complex balance belongs to the cone formula_109. That is, there exists a system with detailed balance, the same reaction mechanism, the same positive equilibrium, that gives the same velocity at state "N". According to cone theorem, for a given state "N", the set of velocities of the semidetailed balance systems coincides with the set of velocities of the detailed balance systems if their reaction mechanisms and equilibria coincide. This means "local equivalence of detailed and complex balance."