Kostrikin's theorem on Engel Lie rings

Statement
Suppose $$p$$ is a prime number. Suppose $$L$$ is a Lie ring that is $$p$$-torsion. Equivalently, $$L$$ is a Lie algebra over the field with $$p$$ elements.

Then, if $$L$$ is a $$(p-1)$$-Engel Lie ring, it is a locally nilpotent Lie ring. In particular, if $$L$$ is finitely generated and $$(p-1)$$-Engel, it is a nilpotent Lie ring.

Related facts

 * Zelmanov's theorem on Engel Lie rings