apply subset_antisymm
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
⊢ ⋂ 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 | ∃ x_1 ∈ n125Set X, List.prod x_1 = x} ⊆ ⋂ s ∈ {K | X ⊆ ↑K}, ↑s