case h
R : Type u
A : Type v
inst✝⁵ : CommSemiring R
inst✝⁴ : Ring A
inst✝³ : Algebra R A
inst✝² : InvolutiveStar R
inst✝¹ : StarRing A
inst✝ : StarModule R A
a : A
x✝ : R
⊢ x✝ ∈ σ (star a) ↔ x✝ ∈ star (σ a)
R : Type u
A : Type v
inst✝⁵ : CommSemiring R
inst✝⁴ : Ring A
inst✝³ : Algebra R A
inst✝² : InvolutiveStar R
inst✝¹ : StarRing A
inst✝ : StarModule R A
a : A
⊢ σ (star a) = star (σ a)
ext
no goals
case h
R : Type u
A : Type v
inst✝⁵ : CommSemiring R
inst✝⁴ : Ring A
inst✝³ : Algebra R A
inst✝² : InvolutiveStar R
inst✝¹ : StarRing A
inst✝ : StarModule R A
a : A
x✝ : R
⊢ x✝ ∈ σ (star a) ↔ x✝ ∈ star (σ a)
simpa only [Set.mem_star, mem_iff, not_iff_not] using star_mem_resolventSet_iff.symm