rw [QuotientGroup.preimage_image_mk_eq_iUnion_smul, mul_comm, Set.iUnion_subtype]
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s✝ t : Finset α
a : α
ht : t.Nonempty
s : Finset α
⊢ QuotientGroup.mk ⁻¹' (QuotientGroup.mk '' ↑s) = ↑s * ↑t.mulStab
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s✝ t : Finset α
a : α
ht : t.Nonempty
s : Finset α
⊢ ⋃ x, ⋃ (hx : x ∈ stabilizer α t), ⟨x, hx⟩ • ↑s = ↑t.mulStab * ↑s