68 lines
1.3 KiB
Text
68 lines
1.3 KiB
Text
x y : Nat
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⊢ x + y = Nat.add y x
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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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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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case h
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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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conv1.lean:139:10-139:13: error: invalid 'lhs' conv tactic, application has only 1 (nondependent) argument(s)
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conv1.lean:142:10-142:15: error: invalid 'arg' conv tactic, application has only 1 (nondependent) argument(s)
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conv1.lean:145:10-145:13: error: invalid 'congr' conv tactic, application or implication expected
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p
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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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