Theorems · Definition · geometry

Affine.Simplex.face

{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} →
                Affine.Simplex k P n → {fs : Finset (Fin (n + 1))} → {m : ℕ} → fs.card = m + 1 → Affine.Simplex k P m

A face of a simplex is a simplex with the given subset of points.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic

Cited by

35 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor