A transverse condition of definable CrG maps

Let G be a definably compact definable C r group and 1 ≤ r < ∞.Let X, Y be affine definable C r G manifolds such that Y is definably compact and without boundary.We prove that for every definable C r G map f : X → Y and for every definable C r G submanifold Z of Y , there exists a definable C r-1 G map h : X → Y such that h is definably C r-1 G homotopic to f and h and h|∂X are transverse to Z.