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

State before:
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ha : a ∈ s.mulStab
⊢ 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 : Group α
inst✝ : DecidableEq α
t : Finset α
a : α
ha : a ∈ ∅.mulStab
⊢ a • ∅.mulStab = ∅.mulStab

case inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ha : a ∈ s.mulStab
hs : s.Nonempty
⊢ a • s.mulStab = s.mulStab

State before:
case inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ha : a ∈ s.mulStab
hs : s.Nonempty
⊢ a • s.mulStab = s.mulStab
Tactic:
rw [← mem_coe, coe_mulStab hs, SetLike.mem_coe] at ha
State after:
case inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ha : a ∈ stabilizer α s
hs : s.Nonempty
⊢ a • s.mulStab = s.mulStab

State before:
case inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ha : a ∈ stabilizer α s
hs : s.Nonempty
⊢ a • s.mulStab = s.mulStab
Tactic:
rw [← coe_inj, coe_smul_finset, coe_mulStab hs, Subgroup.smul_coe ha]
State after:
no goals

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