exact congrArg₂ _ (congrArg₂ _ (Nat.mul_mod_mul_left _ _ _) (Nat.mod_eq_of_lt (lt_of_lt_of_le (Nat.mod_lt _ (Nat.zero_lt_succ _)) (Nat.le_mul_of_pos_right (Nat.zero_lt_succ _))))) rfl
case h₂.h₂.h₁
a b✝ c✝ b c : ℕ
⊢ ((b + 1) * (a / (b + 1)) % ((b + 1) * (c + 1)) + a % (b + 1) % ((b + 1) * (c + 1))) % ((b + 1) * (c + 1)) = ?h₂.h₂.b

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

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