A Groszek-Laver pair of undistinguishable E0-classes

A generic extension $L[x,y]$ of $L$ by reals $x,y$ is defined, in which the union of $\mathsf E_0$-classes of $x$ and $y$ is a $\Pi^1_2$ set, but neither of these two $\mathsf E_0$-classes is separately ordinal-definable.

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