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feat: add Chapter 10 formalization on Hilbert’s third problem - #157

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AItoBit wants to merge 3 commits into
mo271:mainfrom
AItoBit:patch-4
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AItoBit wants to merge 3 commits into
mo271:mainfrom
AItoBit:patch-4

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@AItoBit AItoBit commented Oct 1, 2026

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Adds a single Lean 4 file covering results from Chapter 10 of Proofs from THE BOOK.

Includes:

  • Cone Lemma and Fourier–Motzkin elimination.
  • Pearl Lemma and Bricard’s condition.
  • Dihedral-angle calculations and tetrahedron examples.
  • Geometric decomposition definitions and polytope results.
  • Minkowski–Weyl characterization of convex polytopes.

The Hilbert’s third problem result uses an abstract segment-and-angle decomposition model. Geometric equidecomposability is defined separately; the file does not establish the bridge from arbitrary geometric decompositions to this model.

Validation: the complete file compiles with zero errors and zero warnings using Lean 4.35.0-rc3 and Mathlib commit 738e62b. No sorry, admit, added axioms, unsafe declarations, or native_decide.

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