apply Eq.trans
a b✝ c✝ b c : ℕ
⊢ a % ((b + 1) * (c + 1)) = (b + 1) * (a / (b + 1) % (c + 1)) + a % (b + 1)
case h₁
a b✝ c✝ b c : ℕ
⊢ a % ((b + 1) * (c + 1)) = ?b

case h₂
a b✝ c✝ b c : ℕ
⊢ ?b = (b + 1) * (a / (b + 1) % (c + 1)) + a % (b + 1)

case b
a b✝ c✝ b c : ℕ
⊢ ℕ