Just a wishlist of things I'd like to be able to prove. Feel free to add to it.

• ∀ (Pi : Bᵣ 2) (V : Bᵣ 3), (∃ x : Bᵣ 1, x ^ Pi = V) ↔ ⟨V * Pi⟩_3 = 0
  Read: a bivector lies fully within a trivector if the 3-grade part of the product is zero