intro x hx
case a
G : Type u_1
inst✝ : Group G
X : Set G
⊢ {x | ∃ x_1 ∈ n125Set X, List.prod x_1 = x} ⊆ ⋂ s ∈ {K | X ⊆ ↑K}, ↑s
case a
G : Type u_1
inst✝ : Group G
X : Set G
x : G
hx : x ∈ {x | ∃ x_1 ∈ n125Set X, List.prod x_1 = x}
⊢ x ∈ ⋂ s ∈ {K | X ⊆ ↑K}, ↑s