simpa only [coe_sort_coe, ← coe_mul, Fintype.card_prod, Fintype.card_coe, Fintype.card_ofFinset,
  toFinset_coe, mem_image, Set.mem_image, mem_coe, forall_const, eq_comm]
  using Fintype.card_congr temp
case inr
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s✝ t✝ : Finset α
a : α
s t : Finset α
ht : t.Nonempty
this : ↑(QuotientGroup.mk ⁻¹' (QuotientGroup.mk '' ↑s)) ≃ ↥(stabilizer α t) × ↑(QuotientGroup.mk '' ↑s)
that : ↥(stabilizer α t) = { x // x ∈ t.mulStab }
temp : ↑(↑s * ↑t.mulStab) ≃ { x // x ∈ t.mulStab } × ↑(QuotientGroup.mk '' ↑s)
⊢ t.mulStab.card * (image QuotientGroup.mk s).card = (s * t.mulStab).card
no goals