  Thanks to Hrushovski-Loeser's work on motivic Milnor fibers, we give a
model-theoretic proof for the motivic Thom-Sebastiani theorem in the case of
regular functions. Moreover, slightly extending of Hrushovski-Loeser's
construction adjusted to Sebag, Loeser and Nicaise's motivic integration for
formal schemes and rigid varieties, we formulate and prove an analogous result
for formal functions. The latter is meaningful as it has been a crucial element
of constructing Kontsevich-Soibelman's theory of motivic Donaldson-Thomas
invariants.
