Theorems · Theorem · geometry

vadd_left_mem_affineSpan_pair

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {p₁ p₂ : P} {v : V}, v +ᵥ p₁ ∈ line[k, p₁, p₂] ↔ ∃ r, r • (p₂ -ᵥ p₁) = v

A vector added to the first point lies in the affine span of two points if and only if it is a multiple of their difference.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

4 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor