Set: pp::colors
  Set: pp::unicode
  Imported 'tactic'
  Using: Nat
  Proved: add_assoc
Nat::add_zerol : ∀ a : ℕ, 0 + a = a
Nat::add_succl : ∀ a b : ℕ, a + 1 + b = a + b + 1
@eq_id : ∀ (A : (Type U)) (a : A), a = a ↔ ⊤
theorem add_assoc (a b c : ℕ) : a + (b + c) = a + b + c :=
    Nat::induction_on
        a
        (let have_expr : 0 + (b + c) = 0 + b + c :=
                 eqt_elim (trans (congr (congr2 eq (Nat::add_zerol (b + c)))
                                        (congr1 c (congr2 Nat::add (Nat::add_zerol b))))
                                 (eq_id (b + c)))
         in have_expr)
        (λ (n : ℕ) (iH : n + (b + c) = n + b + c),
           let have_expr : n + 1 + (b + c) = n + 1 + b + c :=
                   eqt_elim (trans (congr (congr2 eq (trans (Nat::add_succl n (b + c)) (congr1 1 (congr2 Nat::add iH))))
                                          (trans (congr1 c (congr2 Nat::add (Nat::add_succl n b)))
                                                 (Nat::add_succl (n + b) c)))
                                   (eq_id (n + b + c + 1)))
           in have_expr)