| import OAI.Geometry.CylinderCovering.Rational.FieldDefinitions |
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| namespace OAI |
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| namespace SlopeRational |
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| noncomputable section |
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| def inverseRectangle (d : ℝ) : Set Plane := |
| {z | |z 0| ≤ 1 ∧ -1 ≤ z 1 ∧ z 1 ≤ 1 / 2 + d / 2} |
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| def tiltedMap (d s : ℝ) (z : Plane) : Plane := z + s • field d z |
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| def RectangleInversionAt (d : ℝ) : Prop := |
| ∃ δ : ℝ, 0 < δ ∧ ∀ s : ℝ, |s| < δ → |
| (∀ y t : ℝ, |y| ≤ 1 / 2 → |t| ≤ 1 / 2 → |
| ∃! p : Plane, p ∈ inverseRectangle d ∧ tiltedMap d s p = vec2 y t) ∧ |
| (∀ p ∈ inverseRectangle d, ∀ q ∈ inverseRectangle d, |
| (tiltedMap d s p) 0 = (tiltedMap d s q) 0 → |
| (tiltedMap d s p) 1 < (tiltedMap d s q) 1 → p 1 < q 1) |
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| def RectangleInversionStatement : Prop := |
| ∀ d : ℝ, 0 < d → RectangleInversionAt d |
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| def RectangleWedgeStatement : Prop := |
| ∀ d : ℝ, 0 < d → ∃ δ : ℝ, 0 < δ ∧ ∀ s : ℝ, |s| < δ → |
| ∀ p ∈ inverseRectangle d, tiltedMap d s p ∈ wedge ↔ p ∈ wedge |
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| end |
| end SlopeRational |
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| end OAI |
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|
