openAI-math-dataset / lean /OAI /Geometry /ProjectionVolume /CounterexampleComparison.lean
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import OAI.Geometry.ProjectionVolume.ProductCounterexample
import OAI.Geometry.ProjectionVolume.SimplexValue
namespace OAI
namespace Paper092
theorem standardSimplex_normalizedProjectionVolume_lt_productWitness :
normalizedProjectionVolume (standardSimplex 20) <
normalizedProjectionVolume productWitness := by
rw [standardSimplex_normalizedProjectionVolume 20 (by norm_num),
productWitness_normalizedProjectionVolume]
exact dimension_twenty_strict
end Paper092
end OAI