Theorems · Theorem · geometry

Affine.Simplex.face_points

∀ {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} (s : Affine.Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h : fs.card = m + 1)
  (i : Fin (m + 1)), (s.face h).points i = s.points ((fs.orderEmbOfFin h) i)

The points of a face of a simplex are given by mono_of_fin.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic

Cited by

2 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor