  The 3-d Z(2) lattice gauge-Higgs theory is cast in a partial axial gauge
leaving a residual Z(2) symmetry, global in two directions and local in one. It
is shown both analytically and numerically that this symmetry breaks
spontaneously in the Higgs phase and is unbroken in the confinement phase.
Therefore they must be separated everywhere by a phase transition, in
contradiction to a theorem by Fradkin and Shenker. It relied on a fully fixed
unitary gauge, which prohibits this phase transition explicitly. Thus the
unfixed gauge theory is not, in this case, equivalent to the unitary-gauge
version.
