Inversion pullback: $(XY)^{m+1}P_\beta(c/X,\bar c/Y)=k\,P_\alpha$, $|\alpha|=|\beta|=1$, forces $|c|=1$, $\beta=\alpha$

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Inversion pullback: $(XY)^{m+1}P_\beta(c/X,\bar c/Y)=k\,P_\alpha$, $|\alpha|=|\beta|=1$, forces $|c|=1$, $\beta=\alpha$ · Prove2Me