Set: pp::colors
  Set: pp::unicode
  Defined: double
⊤
⊤
9
⊥
2 + 2 + (2 + 2) + 1 ≥ 3
3 ≤ 2 * 2 + 2 * 2 + 2 * 2 + 2 * 2 + 1
  Assumed: a
  Assumed: b
  Assumed: c
  Assumed: d
  Imported 'if_then_else'
a * c + a * d + b * c + b * d
trans (Nat::distributel a b (c + d))
      (trans (congr (congr2 Nat::add (Nat::distributer a c d)) (Nat::distributer b c d))
             (Nat::add_assoc (a * c + a * d) (b * c) (b * d)))
  Proved: congr2_congr1
  Proved: congr2_congr2
  Proved: congr1_congr2
⊤
trans (congr (congr2 eq
                     (congr1 10
                             (congr2 Nat::add (trans (congr2 (ite (a > 0) b) (Nat::add_zeror b)) (if_a_a (a > 0) b)))))
             (congr1 10 (congr2 Nat::add (if_a_a (a > 0) b))))
      (eq_id (b + 10))
let κ::1 := congr2 (λ x : ℕ → ℕ, eq (x 10))
                    (congr2 Nat::add (trans (congr2 (ite (a > 0) b) (Nat::add_zeror b)) (if_a_a (a > 0) b)))
in trans (congr κ::1 (congr1 10 (congr2 Nat::add (if_a_a (a > 0) b)))) (eq_id (b + 10))
a * a + a * b + b * a + b * b
⊤ → ⊥	refl (⊤ → ⊥)
⊤ → ⊤	refl (⊤ → ⊤)
⊥ → ⊥	refl (⊥ → ⊥)
⊥	refl ⊥