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Rewrite ending paragraph of symm breaking section
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ccodel committed Jun 10, 2024
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This concludes the proof.
\end{proof}

We had quite some difficulty formalizing the symmetry-breaking argument.
We spent many hours around a whiteboard,
simplifying the argument to minimize the amount of theory we would need to develop.
The projective transformation in Step 3 was particularly difficult to wrangle.
This step, and those after it, requires careful bookkeeping around the distinguished point $p_1$.

Once these details were worked out,
the proof was relatively straightforward, albeit long and tedious.
Each step of the proof justifies not only that a new property is achieved,
but also that all properties from previous steps are preserved.
As a result, the proof burden was substantial.
Compared to the symmetry-breaking transformation described by Heule and Scheucher,
our transformation is simpler.
Nonetheless, proving the above theorem in Lean was tedious,
as we had to show that the properties from the previous steps were preserved at each new step,
which carried substantial proof burden.
In particular, steps 3 through 6 required careful bookkeeping and special handling of the distinguished point~$p_1$.

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