Proof of Karnaugh(k-map) method

Question

How to prove that by grouping the largest number of 1`s in a Karnaugh Map one can always get a minimal DNF?

I understand that it reduces the number of symbols, but I can`t show the above fact is true.

Answer 1

\begin{array}{|c|c|c|c|} \hline &1\\ \hline &1&1&1\\ \hline 1&1&1\\ \hline &&1\\ \hline \end{array}