105 lines
5.1 KiB
Text
105 lines
5.1 KiB
Text
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Set: pp::colors
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Set: pp::unicode
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Imported 'macros'
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Using: Nat
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Assumed: Induction
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Failed to solve
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⊢ (?M::10 ≈ @mp) ⊕ (?M::10 ≈ eq::@mp) ⊕ (?M::10 ≈ forall::@elim)
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(line: 11: pos: 5) Overloading at
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(forall::@elim | eq::@mp | @mp) _ _ Induction _
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Failed to solve
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⊢ (ℕ → Bool) → Bool ≺ Bool
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(line: 11: pos: 5) Type of argument 3 must be convertible to the expected type in the application of
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@mp
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with arguments:
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?M::7
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λ P : ℕ → Bool, P 0 ⇒ (∀ n : ℕ, P n ⇒ P (n + 1)) ⇒ (∀ n : ℕ, P n)
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Induction
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?M::9
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Failed to solve
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⊢ ∀ P : ℕ → Bool, P 0 ⇒ (∀ n : ℕ, P n ⇒ P (n + 1)) ⇒ (∀ n : ℕ, P n) ≺ ?M::7 == ?M::8
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(line: 11: pos: 5) Type of argument 3 must be convertible to the expected type in the application of
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eq::@mp
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with arguments:
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?M::7
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?M::8
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Induction
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?M::9
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Failed to solve
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⊢ (?M::17 ≈ @mp) ⊕ (?M::17 ≈ eq::@mp) ⊕ (?M::17 ≈ forall::@elim)
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(line: 12: pos: 6) Overloading at
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(forall::@elim | eq::@mp | @mp)
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_
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_
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((forall::@elim | eq::@mp | @mp) _ _ Induction _)
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(forall::intro (λ m : _, Nat::add::zerol m ⋈ symm (Nat::add::zeror m)))
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Failed to solve
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⊢ (?M::34 ≈ @mp) ⊕ (?M::34 ≈ eq::@mp) ⊕ (?M::34 ≈ forall::@elim)
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(line: 15: pos: 5) Overloading at
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let κ::1 := (forall::@elim | eq::@mp | @mp)
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_
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_
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((forall::@elim | eq::@mp | @mp) _ _ Induction _)
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(forall::intro (λ m : _, Nat::add::zerol m ⋈ symm (Nat::add::zeror m))),
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κ::2 := λ n : _,
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discharge
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(λ iH : _,
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forall::intro
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(λ m : _,
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Nat::add::succl n m ⋈ subst (refl (n + m + 1)) iH ⋈
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symm (Nat::add::succr m n)))
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in (forall::@elim | eq::@mp | @mp) _ _ κ::1 (forall::intro κ::2)
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Failed to solve
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⊢ ∀ n : ℕ, ?M::9 n ≺ ∀ n m : ℕ, n + m = m + n
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(line: 15: pos: 5) Type of definition 'Comm1' must be convertible to expected type.
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Failed to solve
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⊢ (∀ n : ℕ, ?M::9 n ⇒ ?M::9 (n + 1)) ⇒ (∀ n : ℕ, ?M::9 n) ≺ ?M::3 == ?M::4
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(line: 15: pos: 5) Type of argument 3 must be convertible to the expected type in the application of
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eq::@mp
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with arguments:
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?M::3
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?M::4
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Induction ◂ ?M::9 ◂ forall::intro (λ m : ℕ, Nat::add::zerol m ⋈ symm (Nat::add::zeror m))
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forall::intro
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(λ n : ℕ,
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discharge
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(λ iH : ?M::20,
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forall::intro
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(λ m : ℕ,
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Nat::add::succl n m ⋈ subst (refl (n + m + 1)) iH ⋈
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symm (Nat::add::succr m n))))
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Failed to solve
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⊢ Bool ≺ ?M::3 → Bool
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(line: 15: pos: 5) Type of argument 3 must be convertible to the expected type in the application of
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forall::@elim
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with arguments:
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?M::3
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∀ n : ℕ, ?M::9 n
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Induction ◂ ?M::9 ◂ forall::intro (λ m : ℕ, Nat::add::zerol m ⋈ symm (Nat::add::zeror m))
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forall::intro
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(λ n : ℕ,
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discharge
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(λ iH : ?M::20,
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forall::intro
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(λ m : ℕ,
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Nat::add::succl n m ⋈ subst (refl (n + m + 1)) iH ⋈
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symm (Nat::add::succr m n))))
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Failed to solve
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⊢ ?M::9 0 ⇒ (∀ n : ℕ, ?M::9 n ⇒ ?M::9 (n + 1)) ⇒ (∀ n : ℕ, ?M::9 n) ≺ ?M::5 == ?M::6
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(line: 12: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
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eq::@mp
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with arguments:
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?M::5
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?M::6
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Induction ◂ ?M::9
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forall::intro (λ m : ℕ, Nat::add::zerol m ⋈ symm (Nat::add::zeror m))
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Failed to solve
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⊢ Bool ≺ ?M::5 → Bool
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(line: 12: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
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forall::@elim
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with arguments:
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?M::5
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(∀ n : ℕ, ?M::9 n ⇒ ?M::9 (n + 1)) ⇒ (∀ n : ℕ, ?M::9 n)
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Induction ◂ ?M::9
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forall::intro (λ m : ℕ, Nat::add::zerol m ⋈ symm (Nat::add::zeror m))
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