Vector space/Finite-dimensional/Linear subspace/Residue class space/Fact

Let ${}K$ denote a field, and let ${}V$ denote a finite-dimensional vector space. Let ${}U\subseteq V$ be a linear subspace.

Then

${}\dim _{K}{\left(V/U\right)}=\dim _{K}{\left(V\right)}-\dim _{K}{\left(U\right)}\,.$

Proof, Write another proof