Theorems · Theorem · geometry

Affine.Simplex.ext

∀ {k : Type u_1} {V : Type u_2} {P : Type u_5} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {n : ℕ} {s1 s2 : Affine.Simplex k P n},
  (∀ (i : Fin (n + 1)), s1.points i = s2.points i) → s1 = s2

Two simplices are equal if they have the same points.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic

Cited by

9 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor