Theorem: MyRing.mul_zero (LeanCourse/MIL/C02_Basics/S02_Proving_Identities_in_Algebraic_Structures.lean)

State before:
R : Type u_1
inst✝ : Ring R
a : R
⊢ a * 0 = 0
Tactic:
have h : a * 0 + a * 0 = a * 0 + 0 := by
  rw [← mul_add, add_zero, add_zero]
State after:
R : Type u_1
inst✝ : Ring R
a : R
h : a * 0 + a * 0 = a * 0 + 0
⊢ a * 0 = 0

State before:
R : Type u_1
inst✝ : Ring R
a : R
h : a * 0 + a * 0 = a * 0 + 0
⊢ a * 0 = 0
Tactic:
rw [add_left_cancel h]
State after:
no goals

State before:
R : Type u_1
inst✝ : Ring R
a : R
⊢ a * 0 + a * 0 = a * 0 + 0
Tactic:
rw [← mul_add, add_zero, add_zero]
State after:
no goals