no goals
G : Type u_1
G' : Type ?u.379936
inst✝² : Group G
inst✝¹ : Group G'
A : Type ?u.379945
inst✝ : AddGroup A
H K : Subgroup G
g : G
⊢ g ∈ normalizer H ↔ ∀ (h : G), h ∈ H ↔ g⁻¹ * h * g ∈ H
rw [← inv_mem_iff (x := g), mem_normalizer_iff, inv_inv]