21 lines
634 B
Text
21 lines
634 B
Text
import Lean
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open Lean.SubExpr
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def ps := [#[], #[0], #[1], #[0,1], #[1,0] , #[0,0], #[1,2,3]]
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theorem Pos.roundtrip :
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true = ps.all fun x => x == (Pos.toArray <| Pos.ofArray <| x)
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:= by native_decide
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theorem Pos.append_roundtrip :
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true = (List.all
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(ps.flatMap fun p => ps.map fun q => (p,q))
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(fun (x,y) => (x ++ y) == (Pos.toArray <| (Pos.append (Pos.ofArray x) (Pos.ofArray y))))
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) := by native_decide
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theorem Pos.stringRoundtrip :
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true = ps.all (fun p =>
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let x := Pos.ofArray p
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some x == (Except.toOption $ Pos.fromString? $ Pos.toString $ x)
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) := by native_decide
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#guard Pos.toString Nat.zero == "/"
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