rw [mem_mulStab (hs.mono subset_union_left), smul_finset_union,
  (mem_mulStab hs).mp (mem_of_mem_inter_left hx),
  (mem_mulStab ht).mp (mem_of_mem_inter_right hx)]
case inr.inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
hs : s.Nonempty
ht : t.Nonempty
x : α
hx : x ∈ s.mulStab ∩ t.mulStab
⊢ x ∈ (s ∪ t).mulStab
no goals