Reevaluating an expression when Assumptions have changed

Question

Is there a way to make this work?

THM = TensorDimensions[M];
Assuming[ Element[M, Vectors[n]], 
    THM
]

Which gives:

TensorDimensions[M]

But I would like it to try executing the expression again, and get

{n}

None of these potential solutions work:

 Assuming[ Element[T, Vectors[n]],
      {THM, 
       Simplify[THM],
       Evaluate[THM]}
 ]  

This works, but is a profoundly ugly kludge:

 Assuming[ Element[T, Vectors[n]],
      {THM /. TensorDimensions[x_] :> TensorDimensions[x]}
 ]  

Can anyone explain what is happening here?

Answer 1

You need to use Update to tell Mathematica that hidden changes have been made that can affect results:

THM=TensorDimensions[M];
Assuming[Element[M,Vectors[n]],THM]

TensorDimensions[M]

Using Update:

Update[M];
Assuming[Element[M,Vectors[n]],THM]

{n}