∀ (a b : ℕ) (flip : Bool) (ha0 : a > 0) (ha4 : a % 4 = 0),
  InvImage (fun x1 x2 => x1 < x2)
    (fun x => PSigma.casesOn x fun a b => PSigma.casesOn b fun b flip => PSigma.casesOn flip fun flip ha0 => a)
    ⟨a / 4, ⟨b, ⟨flip, ⋯⟩⟩⟩ ⟨a, ⟨b, ⟨flip, ha0⟩⟩⟩