b5122b6a7b
This change * moves `termination_by` and `decreasing_by` next to the function they apply to * simplify the syntax of `termination_by` * apply the `decreasing_by` goal to all goals at once, for better interactive use. See the section in `RELEASES.md` for more details and migration advise. This is a hard breaking change, requiring developers to touch every `termination_by` in their code base. We decided to still do it as a hard-breaking change, because supporting both old and new syntax at the same time would be non-trivial, and not save that much. Moreover, this requires changes to some metaprograms that developers might have written, and supporting both syntaxes at the same time would make _their_ migration harder.
26 lines
604 B
Text
26 lines
604 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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decreasing_by apply Nat.lt_succ_self
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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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decreasing_by apply Nat.lt_succ_self
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end
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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 [isEven]
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| succ x ih =>
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unfold isEven
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trace_state
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rw [Nat.mul_succ, Nat.add_succ]
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simp
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unfold isOdd
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trace_state
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simp
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exact ih
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theorem isEven_succ_succ (x : Nat) : isEven (x + 2) = isEven x := by
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conv => lhs; unfold isEven; simp; unfold isOdd; simp
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