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Large-scale molecular-dynamics simulations are performed to study the steady-state yielding dynamics of a well-established simple glass. In contrast to the supercooled state, where the shear stress, sigma, tends to zero at vanishing shear rate, gamma-dot, a stress plateau forms in the glass which extends over about two decades in shear rate. This strongly suggests the existence of a finite dynamic yield stress in the glass, sigma+(T)[equivalent]sigma(T;gamma-dot -->0)>0. Furthermore, the temperature dependence of sigma+ suggests a yield stress discontinuity at a critical temperature of Tc=0.4 in agreement with recent mode coupling theory predictions. The corresponding qualitative change of the flow curves enables us to bracket the critical temperature Tc of the theory from above and from below. We scrutinize and support this observation by testing explicitly for the assumptions (affine flow, absence of flow-induced ordering) inherent in the theory. Furthermore, while qualitative similarity is found between the viscosity and the final relaxation time of stress fluctuations, significant quantitative differences are observed in the nonlinear regime.