Theorems · Theorem · geometry

AffineSubspace.mem_affineSpan_singleton

∀ (k : Type u_1) (V : Type u_2) {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [S : AddTorsor V P] {p₁ p₂ : P}, p₁ ∈ affineSpan k {p₂} ↔ p₁ = p₂

A point is in the affine span of a single point if and only if they are equal.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

3 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor