48 lines
951 B
Text
48 lines
951 B
Text
namespace Ex1
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mutual
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def f : Nat → Bool → Nat
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| n, true => 2 * f n false
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| 0, false => 1
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| n, false => n + g n
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def g (n : Nat) : Nat :=
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if h : n ≠ 0 then
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f (n-1) true
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else
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n
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end
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termination_by'
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invImage
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(fun
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| PSum.inl ⟨n, true⟩ => (n, 2)
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| PSum.inl ⟨n, false⟩ => (n, 1)
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| PSum.inr n => (n, 0))
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$ Prod.lex sizeOfWFRel sizeOfWFRel
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decreasing_by
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simp [invImage, InvImage, Prod.lex, sizeOfWFRel, measure, Nat.lt_wfRel, WellFoundedRelation.rel]
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first
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| apply Prod.Lex.left
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apply Nat.pred_lt
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| apply Prod.Lex.right
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decide
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done -- should fail
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end Ex1
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namespace Ex2
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mutual
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def f : Nat → Bool → Nat
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| n, true => 2 * f n false
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| 0, false => 1
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| n, false => n + g (n+1) -- Error
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def g (n : Nat) : Nat :=
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if h : n ≠ 0 then
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f (n-1) true
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else
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n
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end
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termination_by
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f n b => (n, if b then 2 else 1)
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g n => (n, 0)
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end Ex2
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