File size: 1,118 Bytes
cead56f | 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 28 29 30 31 32 33 34 35 36 37 38 39 40 | import OAI.Geometry.ProjectionBody.ProductFacetGraphs
import OAI.Geometry.ProjectionBody.GraphProjection
namespace OAI
noncomputable section
open scoped RealInnerProductSpace
namespace ProjectionCounterexample
/-- The true projected area scale of each product facet chart. -/
theorem productFacetProjection_normDet (i : Bool × Option (Fin 10))
{u : E 20} (hu : ‖u‖ = 1) :
((project u).toLinearMap.comp (productFacetLinear i)).normDet =
|productFunctional i u| := by
rcases i with ⟨b, i⟩
cases b
· cases i with
| none =>
rw [productFacetLinear_first_sum, graphProjection_normDet _ _ hu,
firstSumGraph_normal_inner]
rfl
| some i =>
rw [productFacetLinear_first_coordinate, coordinateProjection_normDet _ hu]
simp [firstBlock]
· cases i with
| none =>
rw [productFacetLinear_second_sum, graphProjection_normDet _ _ hu,
secondSumGraph_normal_inner]
rfl
| some i =>
rw [productFacetLinear_second_coordinate, coordinateProjection_normDet _ hu]
simp [secondBlock]
end ProjectionCounterexample
end
end OAI
|