refine' ⟨⟨1, SetLike.mem_coe.mpr (one_mem _)⟩, fun h₁ h₂ h₁mem h₂mem => _⟩
G : Type u_1
inst✝ : Group G
H : Subgroup G
⊢ Set.Nonempty ↑H ∧ ∀ (h₁ h₂ : G), h₁ ∈ ↑H → h₂ ∈ ↑H → h₁ * h₂⁻¹ ∈ ↑H
G : Type u_1
inst✝ : Group G
H : Subgroup G
h₁ h₂ : G
h₁mem : h₁ ∈ ↑H
h₂mem : h₂ ∈ ↑H
⊢ h₁ * h₂⁻¹ ∈ ↑H