Theorems · Theorem · geometry

AffineSubspace.vsub_right_mem_direction_iff_mem

∀ {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] {s : AffineSubspace k P} {p : P}, p ∈ s → ∀ (p₂ : P), p₂ -ᵥ p ∈ s.direction ↔ p₂ ∈ s

Given a point in an affine subspace, a result of subtracting that point on the right is in the direction if and only if the other point is in the subspace.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

10 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor