Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_mem

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p : P} {as : AffineSubspace ℝ P},
  s.IsTangentAt p as → ∀ {x : P}, x ∈ as → inner ℝ (x -ᵥ p) (p -ᵥ s.center) = 0

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

2 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor