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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | 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
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