  The lineless power-law emission observed by ASCA from the northeastern rim of
the supernova remnant SN1006 has recently been interpreted as synchrotron
radiation of electrons with energies around 100 TeV. In this letter we
calculate the flux of inverse Compton emission at TeV photon energies that is a
natural consequence of the existence of such high energy electrons and the
cosmic microwave background. We find that the predicted flux is near the
present sensitivity limit of the southern \v Cerenkov telescope CANGAROO, and
should be detectable with the next performance improvements. The spectrum of
SN1006 at a few TeV will be very soft. The existence of such highest energy
electrons in SN1006 may not be a unique to this remnant. We can therefore
conclude that the detection of TeV $\gamma$-ray emission in any supernova
remnant does not necessarily provide evidence for a large number of cosmic ray
nucleons in these objects, and thus is no simple test of cosmic ray origin as
far as nucleons are concerned.
