no goals
F : Type ?u.406937
R : Type u_1
A : Type u_2
B : Type ?u.406946
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : Semiring A
inst✝⁶ : Algebra R A
inst✝⁵ : StarRing A
inst✝⁴ : StarModule R A
inst✝³ : Semiring B
inst✝² : Algebra R B
inst✝¹ : StarRing B
inst✝ : StarModule R B
S : Subalgebra R A
x : A
⊢ star x ∈ star S ↔ x ∈ S
simp only [mem_star_iff, star_star]