no goals
F : Type ?u.702130
R : Type u_2
A : Type u_1
B : Type ?u.702139
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
x : A
⊢ x ∈ ⊥ ↔ x ∈ Set.range ↑(algebraMap R A)
rw [← mem_toSubalgebra, bot_toSubalgebra, Algebra.mem_bot]