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