File size: 1,036 Bytes
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 | import OAI.Geometry.CylinderCovering.Rational.FieldDefinitions
namespace OAI
namespace SlopeRational
noncomputable section
def inverseRectangle (d : ℝ) : Set Plane :=
{z | |z 0| ≤ 1 ∧ -1 ≤ z 1 ∧ z 1 ≤ 1 / 2 + d / 2}
def tiltedMap (d s : ℝ) (z : Plane) : Plane := z + s • field d z
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)
def RectangleInversionStatement : Prop :=
∀ d : ℝ, 0 < d → RectangleInversionAt d
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
end
end SlopeRational
end OAI
|