Proof
Most statements are immediately clear. (2) follows from the fact that if
-
holds, then also
-
holds for every
.
If
,
then this implication can be reversed by multiplication with .
(6). Let be the equation
-
and be the equation
-
If a tuple
satisfies both equations, then it also satisfies the equation
.
And if the tuple satisfies the equations
and ,
then it also satisfies the equation
and .