∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α}
  (self self_1 : GaloisInsertion l u),
  self = self_1 → ∀ (x x_1 : α) (e_x : x = x_1) (a : u (l x) ≤ x), self.choice x a = self_1.choice x_1 ⋯