Theorems · Theorem · geometry

Affine.Simplex.disjoint_interior_closedInterior_face

∀ {k : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] [inst_4 : PartialOrder k] {n : ℕ} (s : Affine.Simplex k P n) {fs : Finset (Fin (n + 1))},
  fs ≠ Finset.univ → ∀ {m : ℕ} (h : fs.card = m + 1), Disjoint s.interior (s.face h).closedInterior

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorPartialOrder