∀ {G : Type u_1} {H : Type u_2} [inst : CommMonoid G] [inst_1 : PartialOrder G] [inst_2 : AddCommMonoid H]
  [inst_3 : PartialOrder H] (e : Additive G ≃+o H),
  (fun e => { toAddEquiv := MulEquiv.toAdditiveLeft e.toMulEquiv, map_le_map_iff' := ⋯ })
      ((fun e => { toMulEquiv := AddEquiv.toMultiplicativeRight e.toAddEquiv, map_le_map_iff' := ⋯ }) e) =
    e