| import OAI.Geometry.RuledCovering.Model | |
| namespace OAI | |
| noncomputable section | |
| open Set MeasureTheory | |
| namespace RuledApproximation | |
| def PhysicalProjectionStatement : Prop := | |
| ∀ (h : ℝ) (T : Set Plane) (g : Plane), | |
| 0 < h → Bornology.IsBounded T → MeasurableSet T → | |
| ∀ F : Space ≃ᵢ Space, ∃ C : Cylinder, | |
| C.carrier = F '' (firstPhysicalMap h '' auxiliaryCylinder T g) ∧ | |
| C.axis = F.toRealLinearIsometryEquiv | |
| (‖vec3 1 (g 0) (h * g 1)‖⁻¹ • vec3 1 (g 0) (h * g 1)) ∧ | |
| C.area = h * volume.real T * physicalWeight h g ∧ | |
| MeasurableSet C.base ∧ Bornology.IsBounded C.base ∧ volume C.base < ⊤ ∧ | |
| (IsOpen T → IsOpen C.base) ∧ | |
| (IsCompact T → IsCompact C.base) ∧ | |
| (IsParallelogram T → C.parallelogram) | |
| end RuledApproximation | |
| end | |
| end OAI | |