Vector space/Linear subspace/Dimensions/Compare/Fact

Let ${\displaystyle {}V}$ denote a finite-dimensional vector space over a field ${\displaystyle {}K}$. Let ${\displaystyle {}U\subseteq V}$ denote a linear subspace.

Then ${\displaystyle {}U}$ is also finite-dimensional, and the estimate

${\displaystyle {}\dim _{K}{\left(U\right)}\leq \dim _{K}{\left(V\right)}\,}$

holds.