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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 | import OAI.Geometry.CylinderCovering.Caps.FiniteDefinitions
namespace OAI
open Set
noncomputable section
namespace CylinderCovering.HalfheightFinite
lemma profile_nonnegative (r : ℝ) : 0 ≤ profile r := by
unfold profile
positivity
lemma cubicCap_continuous (δ : ℝ) : Continuous (cubicCap δ) := by
unfold cubicCap profile
fun_prop
lemma fractionalCap_continuous (δ : ℝ) : Continuous (fractionalCap δ) := by
unfold fractionalCap profile
fun_prop
lemma cubicCap_positive {δ : ℝ} (hδ : 0 ≤ δ) (r : ℝ) :
0 < cubicCap δ r := by
unfold cubicCap
have hp := profile_nonnegative r
positivity
lemma fractionalCap_positive {δ : ℝ} (hδ : 0 ≤ δ) (r : ℝ) :
0 < fractionalCap δ r := by
unfold fractionalCap
have hp := profile_nonnegative r
positivity
end CylinderCovering.HalfheightFinite
end
end OAI
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