ext
case mpr
G : Type u_1
inst✝ : Group G
A : Set G
g : G
⊢ A = {x | ∃ b ∈ {x | ∃ a ∈ A, g⁻¹ * a = x}, g * b = x}
case mpr.h
G : Type u_1
inst✝ : Group G
A : Set G
g x✝ : G
⊢ x✝ ∈ A ↔ x✝ ∈ {x | ∃ b ∈ {x | ∃ a ∈ A, g⁻¹ * a = x}, g * b = x}