rw [Membership.mem, instMembershipSet]
α : Type u_1
G : group α
hmul_mem : ∀ (a b : α), a ∈ whole_group → b ∈ whole_group → a * b ∈ whole_group
⊢ has_one.one ∈ whole_group
α : Type u_1
G : group α
hmul_mem : ∀ (a b : α), a ∈ whole_group → b ∈ whole_group → a * b ∈ whole_group
⊢ { mem := fun x s => Set.isMember x }.1 has_one.one whole_group