Theorem: MyRing.zero_mul (LeanInRome/S2_Basics/solutions/Solutions_S02_Proving_Identities_in_Algebraic_Structures.lean)

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

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

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