35 lines
1.1 KiB
Text
35 lines
1.1 KiB
Text
import Lean
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open Lean Elab Tactic in
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elab "exact_false" : tactic =>
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closeMainGoal (mkConst ``Bool.false)
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def f (b : Bool := by exact_false) : Nat := bif b then 1 else 0
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example : f false = bif false then 1 else 0 := by rw [f]
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example : f true = bif true then 1 else 0 := by rw [f]
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example (b : Bool) : f b = bif b then 1 else 0 := by rw [f]
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def g (x : Nat) (b : Bool := by exact_false) : Nat :=
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match x with
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| 0 => bif b then 1 else 0
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| x+1 => g x b + 1
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example : g (x+1) true = g x true + 1 := by rw [g]
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example : g (x+1) false = g x false + 1 := by rw [g]
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example : g (x+1) = g x false + 1 := by rw [g]
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example : g (x+1) b = g x b + 1 := by rw [g]
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def foo (x n : Nat) (b : Bool := by exact_false) : Nat :=
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if _ : x < n then
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foo (x+1) n b + 1
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else
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g x b
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termination_by n - x
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example : foo x n true = if _ : x < n then foo (x+1) n true + 1 else g x true := by
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rw [foo]
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example : foo x n b = if _ : x < n then foo (x+1) n b + 1 else g x b := by
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rw [foo]
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example : foo x n false = if _ : x < n then foo (x+1) n false + 1 else g x false := by
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rw [foo]
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