| 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 | |