Theorems · Theorem · geometry

AffineSubspace.direction_sup_eq_sup_direction

∀ {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] {s₁ s₂ : AffineSubspace k P} {p : P},
  p ∈ s₁ → p ∈ s₂ → (s₁ ⊔ s₂).direction = s₁.direction ⊔ s₂.direction

The direction of the sup of two affine subspaces with a common point is the sup of the two directions.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor