The reciprocal inhibition of antagonist muscle upon lateral gaze is explained by -

Sherrington's law of reciprocal innervation According to it, during ocular motility increased flow of innervation to the contracting muscle is accompanied by decreased flow of innervation to the relaxing antagonist muscle. Hering's law of equal innervation According to law in equal and simultaneous innervation flows from the brain to a pair of muscles which contract simultaneously (yoke muscles) in different binocular movements. Ref;A.K.Khurana; 6th Edition; Page no:339