46 lines
741 B
Text
46 lines
741 B
Text
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declare_syntax_cat foo
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variable {m : Type → Type}
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variable [s : Functor m]
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#check @Nat.rec
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#check s.map
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/-
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The following doesn't work because
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```
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variable [r : Monad m]
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#check r.map
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```
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because `Monad.to* methods have bad binder annotations
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-/
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theorem aux (a b c : Nat) (h₁ : a = b) (h₂ : c = b) : a = c := by
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let! aux := h₂.symm
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subst aux
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subst h₁
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exact rfl
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def ex1 : {α : Type} → {a b c : α} → a = b → b = c → a = c :=
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@(by intro α a b c h₁ h₂
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exact Eq.trans h₁ h₂)
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def f1 (x : Nat) : Nat := by
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apply (· + ?hole)
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exact 1
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case hole => exact x
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theorem ex2 (x : Nat) : f1 x = 1 + x :=
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rfl
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def f2 (x : Nat) : Nat := by
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apply Nat.add _
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exact 1
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exact x
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theorem ex3 (x : Nat) : f2 x = x + 1 :=
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rfl
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