Theorems · Theorem · geometry

Affine.Simplex.mongePoint_eq_of_range_eq

∀ {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} {s₁ s₂ : Affine.Simplex ℝ P n},
  Set.range s₁.points = Set.range s₂.points → s₁.mongePoint = s₂.mongePoint

Two simplices with the same points have the same Monge point.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

1 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor