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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 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | import OAI.Geometry.CylinderCovering.Angular.Admissibility
import OAI.Geometry.CylinderCovering.Angular.Aperture
import OAI.Geometry.CylinderCovering.Angular.Cubic
import OAI.Geometry.CylinderCovering.Angular.CubicEstimates
import OAI.Geometry.CylinderCovering.Angular.EqualPartition
import OAI.Geometry.CylinderCovering.Angular.GeneralArea
import OAI.Geometry.CylinderCovering.Angular.GeneralCap
import OAI.Geometry.CylinderCovering.Beams.FullStatement
import OAI.Geometry.CylinderCovering.Beams.PositivePart
import OAI.Geometry.CylinderCovering.Beams.RectangleCylinder
import OAI.Geometry.CylinderCovering.Caps.CoverageBounds
import OAI.Geometry.CylinderCovering.Caps.FiniteCylinders
import OAI.Geometry.CylinderCovering.Convexity.CanonicalRegularSimilarity
import OAI.Geometry.CylinderCovering.Convexity.CompactParallelogramCover
import OAI.Geometry.CylinderCovering.Convexity.ConvexPerturbationInverse
import OAI.Geometry.CylinderCovering.Convexity.FiniteCauchyVariation
import OAI.Geometry.CylinderCovering.Convexity.FinitePlaneMeasure
import OAI.Geometry.CylinderCovering.Convexity.GeneralCapFamily
import OAI.Geometry.CylinderCovering.Convexity.GeneralCapScalarHelpers
import OAI.Geometry.CylinderCovering.Convexity.InverseSqrtBounds
import OAI.Geometry.CylinderCovering.Convexity.OpenThickening
import OAI.Geometry.CylinderCovering.Convexity.RegularSimilarityBasis
import OAI.Geometry.CylinderCovering.Convexity.SpectralNormComparison
import OAI.Geometry.CylinderCovering.Convexity.ThresholdInverse
import OAI.Geometry.CylinderCovering.Cubic.ScalarEstimates
import OAI.Geometry.CylinderCovering.Footprints.Limits
import OAI.Geometry.CylinderCovering.Nilpotent.ExplicitCorollaries
import OAI.Geometry.CylinderCovering.Nilpotent.ZeroProfile
import OAI.Geometry.CylinderCovering.Physical.HalfTilt
import OAI.Geometry.CylinderCovering.Physical.MinimumExamples
import OAI.Geometry.CylinderCovering.Radial.Alignment
import OAI.Geometry.CylinderCovering.Rational.Bundle
import OAI.Geometry.CylinderCovering.Rational.NormalizedCost
import OAI.Geometry.CylinderCovering.Rational.PotentialExamples
import OAI.Geometry.CylinderCovering.Rational.StrictInverse
import OAI.Geometry.CylinderCovering.Rational.UncenteredCoefficients
import OAI.Geometry.CylinderCovering.Results
import OAI.Geometry.CylinderCovering.Simplex.ZeroShift
namespace OAI
namespace CylinderCovering
theorem fourPaperMain :
AngularExplicitStatement ∧
RuledApproximation.HyperbolicStatement ∧
RuledApproximation.NilpotentC1Statement ∧
RegularParallelogramCounterexampleStatement ∧
RegularOpenCounterexampleStatement ∧
RadialSweep.AlignedStatement ∧
RadialSweep.ActualSweepStatement := by
exact ⟨angularExplicit, ruledHistorical.1, nilpotentC1,
regularParallelogramCounterexample, regularOpenCounterexample,
radialAligned, radialActualSweep⟩
end CylinderCovering
end OAI
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