Double of class two Lie cring is class two Lie ring

Statement
Suppose $$L$$ is a fact about::class two Lie cring with abelian group structure denoted additively and cring operation denoted by $$*$$. Then, with the same additive structure, and with Lie bracket:

$$\! [x,y] := 2(x * y)$$

$$L$$ acquires the structure of a fact about::Lie ring of nilpotency class two.

Facts used

 * 1) uses::Skew of class two near-Lie cring is class two Lie ring