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CP violation in mixing occurs whenThe flavour-transition probabilities are proportional to $|q/p{|}^2|g_{-}{|}^2$ for $K^0\to {\bar{K}}^0$, and $|p/q{|}^2|g_{-}{|}^2$ for the reverse. Their inequality remains when decay probability amplitudes themselves conserve CP. The coefficients multiplying the mixed-decay terms in the rate equations encode this asymmetry.

Assume the usual semileptonic flavour selection rule $\Delta S=\Delta Q$, negligible wrong-sign decay probability amplitudes, and equal magnitudes for CP-conjugate allowed probability amplitudes. Then $f_{+}={\pi }^{-}{\ell }^{+}\nu$ is reached directly only from $K^0$, and $f_{-}={\pi }^{+}{\ell }^{-}\bar{\nu }$ only from ${\bar{K}}^0$. Put $|A_{f_{+}}|=|{\bar{A}}_{f_{-}}|=|A|$. The four rates areThere is only one path to each tagged semileptonic channel, so no direct/mixed decay interference survives. The semileptonic wrong-sign mixing asymmetry isIt isolates CP violation in mixing under the stated assumptions. Allowing direct semileptonic CP violation or wrong-sign probability amplitudes would spoil that isolation.^[ref]