Theorems · Theorem · geometry

Affine.Simplex.touchpoint_mem_affineSpan

∀ {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] {n : ℕ} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) (signs : Finset (Fin (n + 1)))
  (i : Fin (n + 1)), s.touchpoint signs i ∈ affineSpan ℝ (Set.range (s.faceOpposite i).points)

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

2 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero