# Invariance under any derivation with partial divided Leibniz condition powers is transitive

From Groupprops

This article gives the statement, and possibly proof, of a Lie ring property (i.e., Lie subring invariant under any derivation with partial divided Leibniz condition powers) satisfying a Lie ring metaproperty (i.e., transitive Lie subring property)

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## Statement

Suppose is a Lie ring and are Lie subrings of with contained in . Suppose is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in . Similarly, suppose is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in .

Then, is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in .