chore: golf proofs about merge #323
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eric-wieser
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chenson2018
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Feb 6, 2026
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| · simp | ||
| · simp | ||
| · grind [cons_merge_cons] |
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I usually try to stay consistent about using simp or grind when they are both just working with theorems that make sense as @[simp, grind =] attributes, e.g.
Suggested change
| · simp | |
| · simp | |
| · grind [cons_merge_cons] | |
| · grind [nil_merge] | |
| · grind [merge_right] | |
| · grind [cons_merge_cons] |
(If these were already annotated upstream I'd just write fun_induction merge <;> grind, but I don't think it's helpful when you are specifying theorems for different branches manually.)
| | case3 => | ||
| grind | ||
| | _ => simp | ||
| simp |
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If you address the simpNF linter by removing ret_merge, this is the only affected proof that then becomes
Suggested change
| simp | |
| grind [List.length_merge] |
| | case2 _ _ _ _ _ ih2 ih1 => exact sorted_merge ih2 ih1 | ||
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| lemma merge_perm (l₁ l₂ : List α) : ⟪merge l₁ l₂⟫ ~ l₁ ++ l₂ := by | ||
| fun_induction merge with |
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Seems like this should follow suit and be grind [List.merge_perm_append]
| /-- Key Lemma: ⌈log2 ⌈n/2⌉⌉ ≤ ⌈log2 n⌉ - 1 for n > 1 -/ | ||
| @[grind →] | ||
| lemma clog2_half_le (n : ℕ) (h : n > 1) : clog 2 ((n + 1) / 2) ≤ clog 2 n - 1 := by | ||
| rw [Nat.clog_of_one_lt one_lt_two h] |
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If golfing, this could just be grind [Nat.clog_of_one_lt].
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The lemmas this golfs are now unused, and could also be deleted.