I may as well give the second step of the reasoning. Suppose we have a 1 kg mass on the table, and suppose (as hypothesised) that Newton’s theory is true. Then the purely gravitational force exerted is
F1 = ma = 1kg x 9.86 m/S^2 = 9.86N
Then suppose also that UA is accelerating the table upwards by 9.86 m/S^2. Then
F2 = ma = 1kg x 9.86 m/S^2 = 9.86N
The principle of resultant force says that the two forces are equivalent to a single force equal to the sum of the forces. Thus
F = F1 + F2 = 9.86N + 9.86N = 19.72N
And forgive me but there is a third step. What is the total acceleration caused by the two forces. Well
a = F/m = 19.72N/1kg = 19.72 m/S^2
Hence, if both UA and Newtonian gravitation are acting upon our 1kg weight, it would accelerate by 19.72 m/S^2 if taken from the table and allowed to fall. But we observe no such thing. QED.
In summary: step 1, understand the idea of resultant force, step 2 understand how UA and Newtonian gravitation exert two separate forces, step 3, understand the resulting acceleration.
[EDIT] And remember this proof is in support of my claim above, that
If the earth is accelerating upwards at 9.8 m/s^2 and the objects upon it are affected by Newtonian gravitation in addition, then the observed downward acceleration would be greater than 9.8 m/s^2. But it isn’t.
Which was precisely the claim that Pete asked me to provide evidence for.