∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G) {a b : AddSubgroup ↥H},
  { toFun := fun H' => ⟨AddSubgroup.map H.subtype H', ⋯⟩, invFun := fun sH' => (↑sH').addSubgroupOf H, left_inv := ⋯,
          right_inv := ⋯ }
        a ≤
      { toFun := fun H' => ⟨AddSubgroup.map H.subtype H', ⋯⟩, invFun := fun sH' => (↑sH').addSubgroupOf H,
          left_inv := ⋯, right_inv := ⋯ }
        b ↔
    a ≤ b