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Do not merge this yet - there are three sorries left on this PR. |
| rw [sq, Finset.sum_mul_sum, ← Finset.sum_product'] | ||
| have dsub : (𝓙₆ t u₁).toFinset.diag ⊆ (𝓙₆ t u₁).toFinset ×ˢ (𝓙₆ t u₁).toFinset := | ||
| Finset.filter_subset .. | ||
| sorry -- was: Finset.filter_subset --.. |
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variable {α} (s t : Finset α) in
theorem _root_.Finset.diag_eq_filter [DecidableEq α] :
Finset.diag s = (s ×ˢ s).filter fun a : α × α => a.fst = a.snd := by
ext; simp +contextual
open Classical in
lemma sum_𝓙₆_indicator_sq_eq {f : Grid X → X → ℝ≥0∞} :
(∑ J ∈ (𝓙₆ t u₁).toFinset, (J : Set X).indicator (f J) x) ^ 2 =
∑ J ∈ (𝓙₆ t u₁).toFinset, (J : Set X).indicator (f J · ^ 2) x := by
rw [sq, Finset.sum_mul_sum, ← Finset.sum_product']
have dsub : (𝓙₆ t u₁).toFinset.diag ⊆ (𝓙₆ t u₁).toFinset ×ˢ (𝓙₆ t u₁).toFinset := by
rw [Finset.diag_eq_filter]
exact Finset.filter_subset ..
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Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
grunweg
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Jan 19, 2026
| _ ≤ _ := by | ||
| gcongr; rw [edist_dist]; apply ofReal_le_of_le_toReal | ||
| rw [toReal_div, toReal_ofNat]; linarith | ||
| replace dnt := @dnt x |
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@fpvandoorn Do you know how difficult it would be to make finiteness support this?
Prior to this line, dnt has the form ∀ {z : X}, depth O z ≠ ⊤; finiteness needs the statement for x.
Adding it as an extra term feels fine to me, so perhaps the answer should just be "wontfix".
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This sounds like it falls well within the scope of aesop, so I don't know why this wouldn't work. Is it related to argument explicitness?
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pushforSetmembership leanprover-community/mathlib4#34023 be used to golf some proofs?finiteness [h, h']syntax leanprover-community/mathlib4#34039 (finiteness [h, h']syntax) is merged, it will also be interesting to try using it more.