Morse theory in definably complete d-minimal structures

Consider a definable complete d-minimal expansion (F, <, +, ·, 0, 1, ,) of an oredered field F. Let X be a definably compact definably normal definable Cʳ manifold and 2 ≤ r <∞. We prove that the set of definable Morse functions is open and dense in the set of definable Cʳ functions on X with respect to the definable C² topology.