Theorems · Theorem · geometry

Affine.Simplex.ExcenterExists.touchpoint_map

∀ {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] {V₂ : Type u_3} {P₂ : Type u_4} [inst_4 : NormedAddCommGroup V₂]
  [inst_5 : InnerProductSpace ℝ V₂] [inst_6 : MetricSpace P₂] [inst_7 : NormedAddTorsor V₂ P₂] {n : ℕ}
  [inst_8 : NeZero n] {s : Affine.Simplex ℝ P n} {signs : Finset (Fin (n + 1))},
  s.ExcenterExists signs →
    ∀ (f : P →ᵃⁱ[ℝ] P₂) (i : Fin (n + 1)), (s.map f.toAffineMap ⋯).touchpoint signs i = f (s.touchpoint signs i)

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

2 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero