∀ {G : Type u_2} {G' : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [inst_2 : AddCommGroup G']
  [inst_3 : LinearOrder G'] (x : G) (y : G') (hxc : AddSubgroup.closure {x} = AddSubgroup.closure {max x (-x)})
  (hyc : AddSubgroup.closure {y} = AddSubgroup.closure {max y (-y)}) (a : ↥(AddSubgroup.closure {y})),
  ⋯.choose • max y (-y) ∈ AddSubgroup.closure {y}