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