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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | import OAI.Geometry.CylinderCovering.Simplex.OverlapVolume
namespace OAI
open Set MeasureTheory CylinderCovering
theorem CylinderCovering.tetrahedron_zero_shift_overlap_volume (v : Fin 4 → Euclidean 3) (hv : AffineIndependent ℝ v)
{u : Euclidean 3} (hu : ‖u‖ = 1) :
volume.real (simplexCarrier v ∩ (fun y => y - (0 : ℝ) • u) '' simplexCarrier v) =
volume.real (simplexCarrier v) := by
simpa only [zero_div, sub_zero, one_pow, one_mul] using
tetrahedron_translated_overlap_volume v hv hu (le_refl (0 : ℝ))
(simplex_longestChord_pos v hv hu)
end OAI
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