I proved by induction that every AVL tree may be colored such that it will be red black tree. The problem is that I can't see an error in my proof. Look at my proof.

Induction for height.
Let's assume that it is truth for each AVL tree of height at most $h$.
Let's consider AVL tree $T$ of height $h+1$. Now, let's consider two subtree of $T$ - $L$ and $R$. We know that $height(R)\le h$ and $height(L)\le h$. Hence using induction hypothesis we conclude that $L$ and $R$ may be colored such that $L$ and $R$ will be red black tree. Then we may paint root - of course black color. Now $T$ is AVL and black tree.

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    $\begingroup$ Do you have a specific question? We don't like "look at my proof!" questions. $\endgroup$ – Raphael Jan 2 '16 at 10:17

Your proof produces a tree in which all nodes are colored black. It doesn't necessarily satisfy the "black height" rule:

Every path from a given node to any of its descendant NIL nodes contains the same number of black nodes.

Not every AVL tree satisfies this condition, for example the Wikipedia example doesn't.

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  • $\begingroup$ Look, at wikipedia example once again. What about following coluouring i.imgur.com/7gWbjl1.png ? $\endgroup$ – user40545 Jan 2 '16 at 11:55
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    $\begingroup$ @user40545 That's not the coloring that your proof produces. $\endgroup$ – Yuval Filmus Jan 2 '16 at 11:57
  • $\begingroup$ Ah, ok I thought that You claied that there is no possiblity to color this graph. $\endgroup$ – user40545 Jan 2 '16 at 16:30

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