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Chapter 12: partial formalization of the slope problem - #160

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AItoBit wants to merge 2 commits into
mo271:mainfrom
AItoBit:patch-6
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AItoBit wants to merge 2 commits into
mo271:mainfrom
AItoBit:patch-6

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@AItoBit AItoBit commented Oct 1, 2026

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Summary

  • Replaces the Chapter 12 stub with a kernel-checked, still incomplete development of the slope problem (Aigner–Ziegler, printed pp. 83–87).
  • Defines directions including the vertical slope, proves the 3-slope bound for a noncollinear triple, the even-case reduction, the p. 83 examples, and the letter-crossing counting lemmas from step (3).
  • Does not assert Ungar’s general bound n-1.

Test plan

  • CI: lake build FormalBook.Chapter_12 (and the full project lint) succeeds on Lean 4.35.0-rc3
  • Confirm there are no sorry/admit in FormalBook/Chapter_12.lean
  • Spot-check that the even-case theorem is only an equivalence of statements, not a proof of the boxed slope bound

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