Theorem: MyNat.mul_add (LeanCourse/MIL/C05_Elementary_Number_Theory/solutions/Solutions_S02_Induction_and_Recursion.lean)

State before:
m n k : MyNat
⊢ mul m (add n k) = add (mul m n) (mul m k)
Tactic:
induction' k with k ih
State after:
case zero
m n : MyNat
⊢ mul m (add n zero) = add (mul m n) (mul m zero)

case succ
m n k : MyNat
ih : mul m (add n k) = add (mul m n) (mul m k)
⊢ mul m (add n (succ k)) = add (mul m n) (mul m (succ k))

State before:
case succ
m n k : MyNat
ih : mul m (add n k) = add (mul m n) (mul m k)
⊢ mul m (add n (succ k)) = add (mul m n) (mul m (succ k))
Tactic:
rw [add, mul, mul, ih, add_assoc]
State after:
no goals

State before:
case zero
m n : MyNat
⊢ mul m (add n zero) = add (mul m n) (mul m zero)
Tactic:
rfl
State after:
no goals