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

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

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