Theorem: Calculated image including Ward-operation changes

The retained breaking changes by

If the Ward operation is fixed, $M=0$. If the insertion correction is only a field-independent scalar in fixed normalization coordinates, its ${\mathcal{V}}_{\xi }{J}_f$ image is zero.

Proof. Expand the transformed operation on the transformed insertion through first order in $\hslash$. The cross term $M(c)J(c)$ has order ${\hslash }^2$ and is discarded. The remaining new terms are exactly (eq:image).