Sets · hard

Statement, exactly as the model and Lean see it

theorem lg_target {α : Type u_1} {s : Set α} : ∑ᶠ (i : α) (_ : i ∈ s), 1 = s.ncard := by

Mathlib declaration: finsum_one
Held-out module: Mathlib.Data.Set.Card.Arithmetic
Banned modules (itself + downstream): 6
Reference proof premises (reachable / held-out): 11 / 0

Traces

Each configuration's full record: what was retrieved, what the model wrote, what Lean said back.

Not verified1 model calls · 1 Lean checks · $0.00004

Attempts

sample 0 · round 0Hallucinated theorem1.6 s model time

Proof

rw [finsum_eq_card]
exact ncard_eq_card' s

What Lean printed (this is all the model sees on repair)

4:6: error: Unknown identifier `finsum_eq_card`
3:86: error: unsolved goals
α : Type u_1
s : Set α
⊢ ∑ᶠ (i : α) (_ : i ∈ s), 1 = s.ncard

Reference proof

Mathlib's own source for this declaration, shown for comparison. It may use lemmas the prover is not allowed to use.

@[simp]
lemma finsum_one {s : Set α} : ∑ᶠ i ∈ s, 1 = s.ncard := by
  obtain hs | hs := s.infinite_or_finite
  · rw [hs.ncard]
    by_cases h : 1 = 0
    · simp [h]
    · exact finsum_mem_eq_zero_of_infinite (by simpa [Function.support_const h])
  · simp [finsum_mem_eq_finite_toFinset_sum _ hs, Set.ncard_eq_toFinset_card s hs]