A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend

We show a lower bound for the boundary crossing probability P{∃z∈[0,1]:h(z)+B0(z)>u(z)} with B0 a Brownian bridge, h a trend function and u a boundary function. By that we get also a lower bound for the boundary crossing probability P{∃z∈[0,1]:h(z)+B0(z)