  For gauge theory, the matrix element for any physical process is independent
of the gauge used. Since this is a formal statement and examples are known
where gauge invariance is violated, for any specific process this gauge
invariance needs to be checked by explicit calculation. In this paper, gauge
invariance is found to hold for a large non-trivial class of processes
described by tree diagrams in the standard model -- tree diagrams with two
external $W$ bosons and any number of external Higgs bosons. This verification
of gauge invariance is quite complicated, and is based on a direct study of the
difference between different gauges through induction on the number of external
Higgs bosons.
