calc
  a * (a⁻¹ * a) * a⁻¹ = a * a⁻¹ * (a * a⁻¹) := ?_
  _ = a * a⁻¹ * 1 := ?_
  _ = a * 1 * a⁻¹ := ?_
  _ = a * (a * a⁻¹) * 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
⊢ a * (a⁻¹ * a) * a⁻¹ = a * (a * a⁻¹) * a⁻¹
case calc_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
⊢ a * (a⁻¹ * a) * a⁻¹ = a * a⁻¹ * (a * a⁻¹)

case calc_2
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
⊢ a * a⁻¹ * (a * a⁻¹) = a * a⁻¹ * 1

case calc_3
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
⊢ a * a⁻¹ * 1 = a * 1 * a⁻¹

case calc_4
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
⊢ a * 1 * a⁻¹ = a * (a * a⁻¹) * a⁻¹