simp only [Set.mem_setOf, n125Set] at hx
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
case a
G : Type u_1
inst✝ : Group G
X : Set G
x : G
hx : ∃ x_1, (∀ x ∈ x_1, x ∈ X ∪ X⁻¹) ∧ List.prod x_1 = x
⊢ x ∈ ⋂ s ∈ {K | X ⊆ ↑K}, ↑s