Theorem: Finset.mulStab_smul (LeanCamCombi/Kneser/MulStab.lean)

State before:
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s✝ t : Finset α
a✝ a : α
s : Finset α
⊢ (a • s).mulStab = s.mulStab
Tactic:
obtain rfl | hs := s.eq_empty_or_nonempty
State after:
case inl
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s t : Finset α
a✝ a : α
⊢ (a • ∅).mulStab = ∅.mulStab

case inr
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s✝ t : Finset α
a✝ a : α
s : Finset α
hs : s.Nonempty
⊢ (a • s).mulStab = s.mulStab

State before:
case inl
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s t : Finset α
a✝ a : α
⊢ (a • ∅).mulStab = ∅.mulStab
Tactic:
simp
State after:
no goals

State before:
case inr
ι : Type u_1
α : Type u_2
inst✝¹ : CommGroup α
inst✝ : DecidableEq α
s✝ t : Finset α
a✝ a : α
s : Finset α
hs : s.Nonempty
⊢ (a • s).mulStab = s.mulStab
Tactic:
rw [← coe_inj, coe_mulStab hs, coe_mulStab hs.smul_finset, stabilizer_smul_eq_right]
State after:
no goals