lean-ja / lean-ja/lean-by-example
induction .. generalizing が必要な例
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Description
theorem MyNat.eq_zero_of_add_eq_zero {m n : MyNat} : m + n = 0 → m = 0 ∧ n = 0 := by
intro h
induction m generalizing n with -- *TODO*: generalizing が必要な例
| zero =>
suffices n = 0 from by simp_all
simp_all
| succ m ih =>
replace ih := @ih (n + 1) -- *TODO*: これは暗黙引数を明示化する例では？
replace ih := ih (show m + (n + 1) = 0 from by rw[← h]; ac_rfl)
simp_all
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Research direction
Start by locating the example containing MyNat.eq_zero_of_add_eq_zero and read the surrounding explanation. Review the two TODO comments, especially whether the second describes explicit application of an implicit argument, and update the example's documentation so both points are accurately explained.
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- documentation
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