0P5W Proof. The lemma follows from the commutativity of the following diagram: E22(m)⊕E2E1(m)\textstyle{E_{2}^{2}(m)\oplus E_{2}E_{1}(m)}E1E2(m)⊕E12(m)\textstyle{E_{1}E_{2}(m)\oplus E_{1}^{2}(m)}E22(m~)⊕E2E1(m~)\textstyle{E_{2}^{2}(\tilde{m})\oplus E_{2}E_{1}(\tilde{m})}E1E2(m~)⊕E12(m~)\textstyle{E_{1}E_{2}(\tilde{m})\oplus E_{1}^{2}(\tilde{m})}σ∘E2π∘τ2\scriptstyle{\sigma\circ E_{2}\pi\circ\tau_{2}}τ1∘E1π∘σ\scriptstyle{\tau_{1}\circ E_{1}\pi\circ\sigma}σ\scriptstyle{\sigma}E22f\scriptstyle{E_{2}^{2}f}E2E1f\scriptstyle{E_{2}E_{1}f}E1E2f\scriptstyle{E_{1}E_{2}f}E12f\scriptstyle{E_{1}^{2}f}σ∘E2π~∘τ2\scriptstyle{\sigma\circ E_{2}\tilde{\pi}\circ\tau_{2}}τ1∘E1π~∘σ\scriptstyle{\tau_{1}\circ E_{1}\tilde{\pi}\circ\sigma}σ\scriptstyle{\sigma} ∎