intro c hi a b
case hs

⊢ ∀ (n : ↑N0),
    (∀ (a b : ↑N0), mul (a, plus (b, n)) = plus (mul (a, b), mul (a, n))) →
      ∀ (a b : ↑N0), mul (a, plus (b, S n)) = plus (mul (a, b), mul (a, S n))
case hs
c : ↑N0
hi : ∀ (a b : ↑N0), mul (a, plus (b, c)) = plus (mul (a, b), mul (a, c))
a b : ↑N0
⊢ mul (a, plus (b, S c)) = plus (mul (a, b), mul (a, S c))