Complex sentence: The local conservation of energy and the consequential variation in rest mass demands that inertial mass is treated under the De Broglie hypothesis as defined by the DeBroglie wavelength of that particle.
Split into simpler sentences: The local conservation of energy, and the consequential variation in rest mass, demand that inertial mass is treated under the De Broglie hypothesis. Mass is defined by the DeBroglie wavelength of that particle.