Theorems · Theorem · geometry

Affine.Simplex.closedInterior_inter_shift_zero

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : PartialOrder k] [IsOrderedAddMonoid k]
  [inst_3 : AddCommGroup V] [inst_4 : AddTorsor V P] [inst_5 : Module k V] {n : ℕ} [NeZero n] (s : Affine.Simplex k P n)
  (i : Fin (n + 1)) [ZeroLEOneClass k],
  s.closedInterior ∩ ↑((affineSpan k (s.points '' {i}ᶜ)).shift (s.points i) 0) = {s.points i}

The base of a simplex shifted with parameter 0 intersects the closed interior only at the vertex.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Shift

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderIsOrderedAddMonoidAddCommGroupAddTorsorModuleNeZeroZeroLEOneClass