To achieve both of a high peak performance and low average power characteristics, frequency-voltage cooperative control processor has been proposed. The processor schedules its operating frequency according to the required computation power. Its operating voltage or body bias voltage is adequately modulated simultaneously to effectively cut down either switching current or leakage current, and it results in reduction of total power dissipation of the processor. Since a frequency-voltage cooperative control processor has two or more operating frequencies, there are countless scheduling methods exist to realize a certain number of cycles by deadline time. This proposition is frequently appears in a hard real-time system. This paper proves two important theorems, which give the power-minimum frequency scheduling method for any types of frequency-voltage cooperative control processor, such as Vdd-control type, Vth-control type and Vdd-Vth-control type processors.