lean-ja / lean-ja/lean-by-example
simp の代わりに明示的に rw を使いたくなる状況の例
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Description
protected theorem MyNat.lt_irrefl (n : MyNat) : ¬ (n < n) := by
intro h
dsimp [(· < ·), MyNat.lt] at *
rw [MyNat.le_iff_add] at *
obtain ⟨k, hk⟩ := h
replace hk : n + (1 + k) = n + 0 := calc
_ = n + 1 + k := by ac_rfl
_ = n := by rw [hk]
_ = n + 0 := by simp
-- 単に simp とすると n+0 → n と単純化されてしまう
rw [MyNat.add_left_cancel_iff] at hk
simp at hk
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No target file or test is named. First locate the relevant example or documentation entry in the repository, then compare it with the supplied Lean snippet; done should be a clear example explaining when explicit rw is preferable to simp.
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