∀ {R : Type u} {A : Type v} {inst : CommSemiring R} {inst_1 : StarRing R} {inst_2 : Semiring A} {inst_3 : StarRing A}
  {inst_4 : Algebra R A} {inst_5 : StarModule R A} (carrier : Set A),
  (∀ (r : R), (algebraMap R A) r ∈ carrier) → 1 ∈ carrier