I suspect that $dim((U_1+U_2)\cap U_3)=dim(U_1\cap U_3)+dim(U_2\cap U_3)$ where $U_1$, $U_2$ and $U_3$ are vector spaces, but I couldn't find a proof or a counterexample. How could I proceed?

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    $\begingroup$ What if $U_1=U_2=U_3$? Can the two sides be still equal? $\endgroup$
    – Anurag A
    Jun 8 '19 at 19:33
  • $\begingroup$ I didn't think the simplest counterexample, thanks $\endgroup$
    – Rhino
    Jun 8 '19 at 19:35

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