166 lines
2.7 KiB
Text
166 lines
2.7 KiB
Text
x y : Nat
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| p (x + y) (y + x + 0)
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x y : Nat
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| x + y = y + x + 0
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x y : Nat
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| x + y = y + x + 0
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x y : Nat
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⊢ x + y = Nat.add y x
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case x
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x y : Nat
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⊢ x + y = Nat.add y x
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case a
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a b : Nat
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| foo (0 + a) (b + 0)
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case a.x
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a b : Nat
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| 0 + a
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case a.y
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a b : Nat
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| b + 0
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a b : Nat
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| a
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case x
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a b : Nat
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| 0 + a
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case y
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a b : Nat
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| b + 0
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case x
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a b : Nat
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| 0 + a
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case x
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a b : Nat
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| a
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case y
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a b : Nat
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| b + 0
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a b : Nat
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| a + b
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case x
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a b : Nat
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| a
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case y
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a b : Nat
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| b
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x y : Nat
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⊢ x + y = Nat.add y x
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x y : Nat
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⊢ Nat.add x y = Nat.add y x
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x y : Nat
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⊢ f x (Nat.add x y) y = y + x
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x y : Nat
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| x + y
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case h.h
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a b : Nat
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| 0 + a + b
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case h.h
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a b : Nat
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| a + b
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case h.h
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a b : Nat
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| 0 + a + b
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p : Nat → Prop
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h : ∀ (a : Nat), p a
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x : Nat
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| p (id (0 + x))
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p : Nat → Prop
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h : ∀ (a : Nat), p a
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x : Nat
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| id (0 + x)
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p : Nat → Prop
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h : ∀ (a : Nat), p a
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x : Nat
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| 0 + x
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case h₁
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p : Prop
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x : Nat
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| x = x → p
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p : Prop
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x : Nat
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⊢ (True → p) → p
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case h
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x : Nat
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| 0 + x
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p : Prop
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x : Nat
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⊢ (True → p) → p
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x y : Nat
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f : Nat → Nat → Nat
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g : Nat → Nat
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h₁ : ∀ (z : Nat), f z z = z
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h₂ : ∀ (x y : Nat), f (g x) (g y) = y
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⊢ f (g y) (f (g x) (g (0 + x))) = x
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x y : Nat
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f : Nat → Nat → Nat
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g : Nat → Nat
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h₁ : ∀ (z : Nat), f z z = z
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h₂ : ∀ (x y : Nat), f (g x) (g y) = y
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⊢ f (g y) (f (g x) (g x)) = x
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x y : Nat
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h : y = 0
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| y + x
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p : Nat → Prop
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x y : Nat
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h1 : y = 0
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h2 : p x
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| y + x
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j : Fin 5
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p : (n : Nat) → Fin n → Prop
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i : Fin 5
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hp : p 5 i
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hi : j = i
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| j
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p : {x : Nat} → Nat → Prop
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x y : Nat
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h1 : y = 0
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h2 : p x
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| y
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p : {x : Nat} → Nat → Prop
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x y : Nat
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h1 : y = 0
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h2 : p x
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| y
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conv1.lean:214:10-214:13: error: invalid 'lhs' conv tactic, application has only 1 (nondependent) argument(s)
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conv1.lean:217:10-217:15: error: invalid 'arg' conv tactic, application has only 1 (nondependent) argument(s)
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conv1.lean:220:10-220:13: error: invalid 'congr' conv tactic, application or implication expected
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p
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conv1.lean:223:10-223:15: error: cannot select argument
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a✝ : Nat := 0
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b✝ : Nat := a✝
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| 0 = 0
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x y z : Nat
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| x + y + z
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x y z : Nat
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| x + y + z
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x y z : Nat
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| x + (y + z)
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x y z : Nat
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| x + y + z
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x y z : Nat
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| y + z
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x y z : Nat
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| y + z
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x y z : Nat
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| x + y + z
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x y z : Nat
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| x + y
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x y z : Nat
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| x + (y + z)
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x y z : Nat
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| x + y
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x y z : Nat
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| y + z
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conv1.lean:241:58-241:83: error: 'pattern' conv tactic failed, pattern was found only 4 times but 5 expected
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conv1.lean:242:58-242:85: error: 'pattern' conv tactic failed, pattern was found only 4 times but 5 expected
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conv1.lean:243:58-243:85: error: 'pattern' conv tactic failed, pattern was found only 3 times but 5 expected
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conv1.lean:244:58-244:87: error: 'pattern' conv tactic failed, pattern was found only 2 times but 5 expected
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