Let $\mathcal{L}$ be a Leibniz algebra. Then the derived series of $\mathcal{L}$ is the series $$\cdots \subset \mathcal{L}^{(2)} \subset \mathcal{L}^{(1)} \subset \mathcal{L}$$ being $$\mathcal{L}^{(1)}≔[\mathcal{L},\mathcal{L}], \hspace{2cm} \mathcal{L}^{(i+1)}≔[\mathcal{L}^{(i)},\mathcal{L}^{(i)}]$$
We recall $\mathcal{L}$ is solvable if $\mathcal{L}^{(n)}=0$ for some $ \in \mathbb{N}$
I´ve readen that it is easy to check that $\mathcal{L}$ is solvable if and only if its associated Lie algebra $ie(\mathcal{L})=\{_ :∈ \mathcal{L}\}$ is solvable
but I can't get the prove. Please, help me.
Thanks in advance and regards