Theorem: Tutorial.inv_mul_cancel_left (Solution/Advanced/Algebra/Lecture1.lean)

State before:
A : Type ?u.2656
G : Type
inst✝¹ : Ring A
inst✝ : Group G
a b : G
⊢ a⁻¹ * (a * b) = b
Tactic:
calc
  a⁻¹ * (a * b) = (a⁻¹ * a) * b := by
    rw [mul_assoc]
    _ = 1 * b := by
    simp
    _ = b := by
    simp
State after:
no goals

State before:
A : Type ?u.2656
G : Type
inst✝¹ : Ring A
inst✝ : Group G
a b : G
⊢ a⁻¹ * (a * b) = a⁻¹ * a * b
Tactic:
rw [mul_assoc]
State after:
no goals

State before:
A : Type ?u.2656
G : Type
inst✝¹ : Ring A
inst✝ : Group G
a b : G
⊢ a⁻¹ * a * b = 1 * b
Tactic:
simp
State after:
no goals

State before:
A : Type ?u.2656
G : Type
inst✝¹ : Ring A
inst✝ : Group G
a b : G
⊢ 1 * b = b
Tactic:
simp
State after:
no goals