19 lines
466 B
Text
19 lines
466 B
Text
mutual
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def isEven : Nat → Bool
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| 0 => true
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| n+1 => isOdd n
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def isOdd : Nat → Bool
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| 0 => false
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| n+1 => isEven n
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end
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termination_by measure fun
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| Sum.inl n => n
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| Sum.inr n => n
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decreasing_by
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simp [measure, invImage, InvImage, Nat.lt_wfRel]
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apply Nat.lt_succ_self
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theorem isEven_double (x : Nat) : isEven (2 * x) = true := by
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induction x with
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| zero => simp
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| succ x ih => simp [Nat.mul_succ, Nat.add_succ, isEven, isOdd, ih]
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