Unique jet determination of CR maps into Nash sets

Let M⊂C^N be a real-analytic CR submanifold, M^′⊂C^N′ a Nash set and E_M^′ the set of points in M^′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p∈M, and for every pair of germs of C^∞-smooth CR maps f,g:(M,p)→M^′, there exists an integer k=k_p such that if f and g have the same k-jets at p, and do not send M into E_M^′, then necessarily f=g. Furthermore, the map p↦k_p may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in C^N into Nash subsets in C^N′ of D'Angelo finite type, for arbitrary N,N^′≥2.