case a
ι : Type ?u.3038576
α : Type u_1
β : Type ?u.3038582
inst✝¹ : DecidableEq α
inst✝ : Fintype α
σ τ : Perm α
a✝ : α
⊢ a✝ ∈ support (σ * τ * σ⁻¹) ↔ a✝ ∈ map (Equiv.toEmbedding σ) (support τ)
ι : Type ?u.3038576
α : Type u_1
β : Type ?u.3038582
inst✝¹ : DecidableEq α
inst✝ : Fintype α
σ τ : Perm α
⊢ support (σ * τ * σ⁻¹) = map (Equiv.toEmbedding σ) (support τ)
ext
case a
ι : Type ?u.3038576
α : Type u_1
β : Type ?u.3038582
inst✝¹ : DecidableEq α
inst✝ : Fintype α
σ τ : Perm α
a✝ : α
⊢ ¬↑σ (↑τ (↑σ⁻¹ a✝)) = a✝ ↔ ¬↑σ (↑τ (↑σ.symm a✝)) = a✝
case a
ι : Type ?u.3038576
α : Type u_1
β : Type ?u.3038582
inst✝¹ : DecidableEq α
inst✝ : Fintype α
σ τ : Perm α
a✝ : α
⊢ a✝ ∈ support (σ * τ * σ⁻¹) ↔ a✝ ∈ map (Equiv.toEmbedding σ) (support τ)
simp only [mem_map_equiv, Perm.coe_mul, Function.comp_apply, Ne.def, Perm.mem_support,
  Equiv.eq_symm_apply]
no goals
case a
ι : Type ?u.3038576
α : Type u_1
β : Type ?u.3038582
inst✝¹ : DecidableEq α
inst✝ : Fintype α
σ τ : Perm α
a✝ : α
⊢ ¬↑σ (↑τ (↑σ⁻¹ a✝)) = a✝ ↔ ¬↑σ (↑τ (↑σ.symm a✝)) = a✝
rfl