ext y
G : Type u_1
inst✝ : Group G
A B : Set G
g : G
⊢ {x | ∃ x_1 ∈ A ∩ B, g * x_1 = x} = {x | ∃ x_1 ∈ A, g * x_1 = x} ∩ {x | ∃ x_1 ∈ B, g * x_1 = x}
case h
G : Type u_1
inst✝ : Group G
A B : Set G
g y : G
⊢ y ∈ {x | ∃ x_1 ∈ A ∩ B, g * x_1 = x} ↔ y ∈ {x | ∃ x_1 ∈ A, g * x_1 = x} ∩ {x | ∃ x_1 ∈ B, g * x_1 = x}