Physically the only relevant (measurable) quantity is
F.
Since
F=2d
A, adding d

to A gives:
A' =
A + d
F' = 2d
A' = 2d
A + 2d(d

)
... but d(d(
anything)) is zero (by the definition of the 'd' operator - see p. 232) so:
F' = 2d
A =
F...i.e. adding d

leaves
F unchanged!