Set: pp::colors
  Set: pp::unicode
  Imported 'tactic'
  Assumed: list
  Assumed: nil
  Assumed: cons
  Assumed: map
  Assumed: map_cons
  Assumed: map_nil
Visit, depth: 1, map (λ x : ℕ, x + 1) (cons 1 (cons 2 nil)) = cons 2 (cons 3 nil)
Visit, depth: 2, @eq
Step: @eq ===> @eq
Visit, depth: 2, map (λ x : ℕ, x + 1) (cons 1 (cons 2 nil))
Visit, depth: 3, @map
Step: @map ===> @map
Visit, depth: 3, λ x : ℕ, x + 1
Visit, depth: 4, 3::1 + 1
Visit, depth: 5, Nat::add
Visit, depth: 5, 3::1
Step: 3::1 ===> 3::1
Visit, depth: 5, 1
Step: 3::1 + 1 ===> 3::1 + 1
Step: λ x : ℕ, x + 1 ===> λ x : ℕ, x + 1
Visit, depth: 3, cons 1 (cons 2 nil)
Visit, depth: 4, @cons
Step: @cons ===> @cons
Visit, depth: 4, 1
Visit, depth: 4, cons 2 nil
Visit, depth: 5, 2
Visit, depth: 5, nil
Visit, depth: 6, @nil
Step: @nil ===> @nil
Step: nil ===> nil
Step: cons 2 nil ===> cons 2 nil
Step: cons 1 (cons 2 nil) ===> cons 1 (cons 2 nil)
Rewrite using: map_cons
  map (λ x : ℕ, x + 1) (cons 1 (cons 2 nil)) ===> cons ((λ x : ℕ, x + 1) 1) (map (λ x : ℕ, x + 1) (cons 2 nil))
Visit, depth: 3, cons ((λ x : ℕ, x + 1) 1) (map (λ x : ℕ, x + 1) (cons 2 nil))
Visit, depth: 4, (λ x : ℕ, x + 1) 1
Visit, depth: 5, 1
Visit, depth: 5, 2
Step: (λ x : ℕ, x + 1) 1 ===> 2
Visit, depth: 4, map (λ x : ℕ, x + 1) (cons 2 nil)
Rewrite using: map_cons
  map (λ x : ℕ, x + 1) (cons 2 nil) ===> cons ((λ x : ℕ, x + 1) 2) (map (λ x : ℕ, x + 1) nil)
Visit, depth: 5, cons ((λ x : ℕ, x + 1) 2) (map (λ x : ℕ, x + 1) nil)
Visit, depth: 6, (λ x : ℕ, x + 1) 2
Visit, depth: 7, 2
Visit, depth: 7, 3
Step: (λ x : ℕ, x + 1) 2 ===> 3
Visit, depth: 6, map (λ x : ℕ, x + 1) nil
Rewrite using: map_nil
  map (λ x : ℕ, x + 1) nil ===> nil
Step: map (λ x : ℕ, x + 1) nil ===> nil
Visit, depth: 6, cons 3 nil
Visit, depth: 7, 3
Step: cons 3 nil ===> cons 3 nil
Step: cons ((λ x : ℕ, x + 1) 2) (map (λ x : ℕ, x + 1) nil) ===> cons 3 nil
Step: map (λ x : ℕ, x + 1) (cons 2 nil) ===> cons 3 nil
Visit, depth: 4, cons 2 (cons 3 nil)
Visit, depth: 5, 2
Step: cons 2 (cons 3 nil) ===> cons 2 (cons 3 nil)
Step: cons ((λ x : ℕ, x + 1) 1) (map (λ x : ℕ, x + 1) (cons 2 nil)) ===> cons 2 (cons 3 nil)
Step: map (λ x : ℕ, x + 1) (cons 1 (cons 2 nil)) ===> cons 2 (cons 3 nil)
Rewrite using: eq_id
  cons 2 (cons 3 nil) = cons 2 (cons 3 nil) ===> ⊤
Visit, depth: 2, ⊤
Step: ⊤ ===> ⊤
Step: map (λ x : ℕ, x + 1) (cons 1 (cons 2 nil)) = cons 2 (cons 3 nil) ===> ⊤
  Proved: T1