Theorems · Theorem · geometry

AffineSubspace.direction_lt_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] {s₁ s₂ : AffineSubspace k P}, s₁ < s₂ → (↑s₁).Nonempty → s₁.direction < s₂.direction

If one nonempty affine subspace is less than another, the same applies to their directions

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor