Bosonic and fermionic dimension versus subdimension conjecture

Let $x$ be an object in a 2-rig. Its bosonic dimension is $n$ when $[?]$; its fermionic dimension is $n$ when $[?]$. Dimension versus subdimension conjecture. If $x$ has bosonic dimension $n$, it has bosonic subdimension $n$. If it has fermionic dimension $n$, it has fermionic subdimension $n$. This conjecture would clarify the relationship between dimension and subdimension in a 2-rig; the source gives no resolution.