Let $E'$ is ellipsoid of dimension $n-1$ that gain as intersection of $E$ and some hyperplane. Let $a_1\leq\cdots\leq a_n$ are halfaxis of $E$ and $b_1\leq\cdots\leq b_{n-1}$ are halfaxis of $E'$. Prove that for any $i$ from $1,\cdots,n-1$ is truth that $a_i\leq b_i\leq a_{i+1}.$

It is obviously for $n=2$. But I can't do induction.


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