feat: add Hadwiger's theorem eval problem#275
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This PR adds Hadwiger's theorem (§31 of Knill's "Some Fundamental Theorems in Mathematics") as a new eval problem: the space of continuous, rigid-motion-invariant valuations on convex bodies in ℝⁿ is (n+1)-dimensional. The problem defines the IsValuation predicate and the valuations submodule; mathlib has ConvexBody but no valuations, intrinsic volumes, or Hadwiger's theorem. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds Hadwiger's theorem as a new lean-eval challenge problem — §31 of Oliver Knill's Some Fundamental Theorems in Mathematics.
The real vector space of continuous, rigid-motion-invariant valuations on convex bodies in
ℝⁿhas dimensionn + 1— a basis being the intrinsic volumes (the coefficients of the Steiner polynomialVol(K + tB)).mathlib has
ConvexBodywith its HausdorffMetricSpacebut no valuations, intrinsic volumes, or Hadwiger's theorem; a search found no formalization in any other proof assistant. The problem defines theIsValuationpredicate (continuity, inclusion–exclusion additivity, linear-isometry and translation invariance) and thevaluationssubmodule.Two encoding notes: the additivity clause is stated over four convex bodies
A B C Dwith↑A = ↑C ∪ ↑D,↑B = ↑C ∩ ↑D(the empty-intersection case is dropped, sinceConvexBodyis nonempty); and theSubmodulemembership-closure fields ofvaluationsare shipped assorry(routine — valuations are closed under sum and scalar multiple).🤖 Prepared with Claude Code