Research proof index

The linear equivalence between Space d.succ and ℝ × Space d extracting the ith coordinate. -/ def slice {d} (i : Fin d.succ) : Space d.succ ≃L[ℝ] ℝ × Space d where toFun x := ⟨x i, ⟨fun j => x (Fin.succAbove i j)⟩⟩ invFun p := ⟨fun j => Fin.insertNthEquiv (fun _ => ℝ) i (p.fst, p.snd) j⟩ map_add' x y := by simp only [Nat.succ_eq_add_one, Prod.mk_add...