Theorems · Theorem · geometry

AffineSubspace.direction_eq_top_iff_of_nonempty

∀ {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] {s : AffineSubspace k P}, (↑s).Nonempty → (s.direction = ⊤ ↔ s = ⊤)

A nonempty affine subspace is ⊤ if and only if its direction is ⊤.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor