  A commonly used theoretical definition of superfluidity in the ground state
of a Bose gas is based on the response of the system to an imposed velocity
field or, equivalently, to twisted boundary conditions in a box. We are able to
carry out this program in the case of a dilute interacting Bose gas in a trap.
We prove that a gas with repulsive interactions is 100% superfluid in the
dilute limit in which the Gross-Pitaevskii equation is exact. This is the first
example in an experimentally realistic continuum model in which superfluidity
is rigorously verified.
