Theorems · Theorem · geometry

AffineSubspace.direction_inf_of_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]
  [S : AddTorsor V P] {s₁ s₂ : AffineSubspace k P} {p : P},
  p ∈ s₁ → p ∈ s₂ → (s₁ ⊓ s₂).direction = s₁.direction ⊓ s₂.direction

If two affine subspaces have a point in common, the direction of their inf equals the inf of their directions.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor