What is the meaning of the $\vdash$ symbol? As seen in the following:
$$\large \lambda=(3,2)\vdash 5$$
I looked it up and in logic the symbol means that what is on the right is provable by what is on the left, but what does it mean in the mathematical context? Does it mean "corresponds to"?

$\lambda\vdash n$ means that:
$$\lambda=(\lambda_1,\dots,\lambda_k)$$
and
$$\sum_\limits{i=1}^k \lambda_i = n$$
