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