simp only at this
G : Type u_1
inst✝³ : One G
inst✝² : Mul G
inst✝¹ : Inv G
inst✝ : Std.Associative fun x x_1 => x * x_1
h1 : ∀ (a : G), a * 1 = a
h2 : ∀ (a : G), a * a⁻¹ = 1
a : G
this✝ : a * (a⁻¹ * a) * a⁻¹ = a * (a * a⁻¹) * a⁻¹
this : (fun x => x * a⁻¹⁻¹) (a * (a⁻¹ * a) * a⁻¹) = (fun x => x * a⁻¹⁻¹) (a * (a * a⁻¹) * a⁻¹)
⊢ a * (a⁻¹ * a) = a * (a * a⁻¹)
G : Type u_1
inst✝³ : One G
inst✝² : Mul G
inst✝¹ : Inv G
inst✝ : Std.Associative fun x x_1 => x * x_1
h1 : ∀ (a : G), a * 1 = a
h2 : ∀ (a : G), a * a⁻¹ = 1
a : G
this✝ : a * (a⁻¹ * a) * a⁻¹ = a * (a * a⁻¹) * a⁻¹
this : a * (a⁻¹ * a) * a⁻¹ * a⁻¹⁻¹ = a * (a * a⁻¹) * a⁻¹ * a⁻¹⁻¹
⊢ a * (a⁻¹ * a) = a * (a * a⁻¹)