Theorems · Definition · geometry

EuclideanGeometry.Sphere.IsTangentAt.casesOn

{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} →
                  {motive : s.IsTangentAt p as → Sort u} →
                    (t : s.IsTangentAt p as) →
                      ((mem_sphere : p ∈ s) → (mem_space : p ∈ as) → (le_orthRadius : as ≤ s.orthRadius p) → motive ⋯) →
                        motive t

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

3 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor