First checking some basic definitions:
Is [Zhuk]'s f pi infinity the same as the one defined at the start of Section 7? True
Is [Bodirsky, Vucaj, Zhuk]'s f pi infinity the same as the one defined at the start of Section 7? True
Is [Bodirsky, Vucaj, Zhuk]'s m the same as the one used in Theorem 7.6? True

Now checking Lemma 7.1:
The solution set constructed in the proof of Lemma 7.1 for f pi infinity is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 2], [0, 0, 1, 0], [0, 0, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0], [0, 0, 2, 1], [0, 0, 2, 2], [0, 1, 0, 0], [0, 1, 1, 1], [0, 1, 2, 2], [0, 2, 0, 0], [0, 2, 1, 1], [0, 2, 2, 2], [1, 0, 0, 0], [1, 0, 1, 1], [1, 0, 2, 2], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 0, 2], [1, 1, 1, 0], [1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 0], [1, 1, 2, 1], [1, 1, 2, 2], [1, 2, 0, 0], [1, 2, 1, 1], [1, 2, 2, 2], [2, 0, 0, 0], [2, 0, 1, 1], [2, 0, 2, 2], [2, 1, 0, 0], [2, 1, 1, 1], [2, 1, 2, 2], [2, 2, 0, 0], [2, 2, 0, 1], [2, 2, 0, 2], [2, 2, 1, 0], [2, 2, 1, 1], [2, 2, 1, 2], [2, 2, 2, 0], [2, 2, 2, 1], [2, 2, 2, 2]]
Solution of equations in Lemma 7.1 with f pi infinity equals Delta? True

The solution set constructed in the proof of Lemma 7.1 for the dual of f pi infinity is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 2], [0, 0, 1, 0], [0, 0, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0], [0, 0, 2, 1], [0, 0, 2, 2], [0, 1, 0, 0], [0, 1, 1, 1], [0, 1, 2, 2], [0, 2, 0, 0], [0, 2, 1, 1], [0, 2, 2, 2], [1, 0, 0, 0], [1, 0, 1, 1], [1, 0, 2, 2], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 0, 2], [1, 1, 1, 0], [1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 0], [1, 1, 2, 1], [1, 1, 2, 2], [1, 2, 0, 0], [1, 2, 1, 1], [1, 2, 2, 2], [2, 0, 0, 0], [2, 0, 1, 1], [2, 0, 2, 2], [2, 1, 0, 0], [2, 1, 1, 1], [2, 1, 2, 2], [2, 2, 0, 0], [2, 2, 0, 1], [2, 2, 0, 2], [2, 2, 1, 0], [2, 2, 1, 1], [2, 2, 1, 2], [2, 2, 2, 0], [2, 2, 2, 1], [2, 2, 2, 2]]
Solution of equations in Lemma 7.1 with dual of f pi infinity equals Delta? True

Now checking Theorem 7.6:
The solution set constructed in the proof of Theorem 7.6 for m is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 2], [0, 0, 1, 0], [0, 0, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0], [0, 0, 2, 1], [0, 0, 2, 2], [0, 1, 0, 0], [0, 1, 1, 1], [0, 1, 2, 2], [0, 2, 0, 0], [0, 2, 1, 1], [0, 2, 2, 2], [1, 0, 0, 0], [1, 0, 1, 1], [1, 0, 2, 2], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 0, 2], [1, 1, 1, 0], [1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 0], [1, 1, 2, 1], [1, 1, 2, 2], [1, 2, 0, 0], [1, 2, 1, 1], [1, 2, 2, 2], [2, 0, 0, 0], [2, 0, 1, 1], [2, 0, 2, 2], [2, 1, 0, 0], [2, 1, 1, 1], [2, 1, 2, 2], [2, 2, 0, 0], [2, 2, 0, 1], [2, 2, 0, 2], [2, 2, 1, 0], [2, 2, 1, 1], [2, 2, 1, 2], [2, 2, 2, 0], [2, 2, 2, 1], [2, 2, 2, 2]]
Solution of equations in Theorem 7.6 with m equals Delta? True

Now checking Proposition 8.2:
The solution set constructed in the proof of Proposition 8.2 for f is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 2], [0, 0, 1, 0], [0, 0, 1, 1], [0, 0, 1, 2], [0, 0, 2, 0], [0, 0, 2, 1], [0, 0, 2, 2], [0, 1, 0, 0], [0, 1, 1, 1], [0, 1, 2, 2], [0, 2, 0, 0], [0, 2, 1, 1], [0, 2, 2, 2], [1, 0, 0, 0], [1, 0, 1, 1], [1, 0, 2, 2], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 0, 2], [1, 1, 1, 0], [1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 0], [1, 1, 2, 1], [1, 1, 2, 2], [1, 2, 0, 0], [1, 2, 1, 1], [1, 2, 2, 2], [2, 0, 0, 0], [2, 0, 1, 1], [2, 0, 2, 2], [2, 1, 0, 0], [2, 1, 1, 1], [2, 1, 2, 2], [2, 2, 0, 0], [2, 2, 0, 1], [2, 2, 0, 2], [2, 2, 1, 0], [2, 2, 1, 1], [2, 2, 1, 2], [2, 2, 2, 0], [2, 2, 2, 1], [2, 2, 2, 2]]
Solution of equations in Proposition 8.2 with f infinity equals Delta? True

Now checking Remark 6.7:
The solution set constructed in Remark 6.7 for the majority operation h is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 1, 1], [1, 0, 0, 0], [1, 0, 1, 1], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 1, 0], [1, 1, 1, 1]]
Solution of equations in Remark 6.7 with majority operation h equals Delta? True

The solution set constructed in Remark 6.7 for the ternary operation t is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 1, 1], [1, 0, 0, 0], [1, 0, 1, 1], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 1, 0], [1, 1, 1, 1]]
Solution of equations in Remark 6.7 with ternary operation t equals Delta? True

The solution set constructed in Remark 6.7 for the dual of the ternary operation t is
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 1, 1], [1, 0, 0, 0], [1, 0, 1, 1], [1, 1, 0, 0], [1, 1, 0, 1], [1, 1, 1, 0], [1, 1, 1, 1]]
Solution of equations in Remark 6.7 with the dual of the ternary operation t equals Delta? True

The claim (implication) about non-definability of Delta via a single equation f==g in Remark 6.7 is True

