Theorems / mh_sets_77230d

Mathlib held-out

Sets · medium

Statement, exactly as the model and Lean see it
theorem lg_target {α : Type u_1} {β : Type u_2} {c : Set (Set α)} (hc : IsChain (fun x1 x2 => x1 ⊆ x2) c) [PartialOrder β] [OrderBot β] (f : α → β) : (⋃ s ∈ c, s).PairwiseDisjoint f ↔ ∀ s ∈ c, s.PairwiseDisjoint f := by
Mathlib declaration
IsChain.pairwiseDisjoint_iUnion₂
Held-out module
Mathlib.Data.Set.Pairwise.Chain
Banned modules (itself + downstream)
1
Reference proof premises (reachable / held-out)
0 / 1

Traces

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

No configuration has attempted this theorem yet.

Reference proof

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

lemma pairwiseDisjoint_iUnion₂ [PartialOrder β] [OrderBot β] (f : α → β) :
    (⋃ s ∈ c, s).PairwiseDisjoint f ↔ ∀ s ∈ c, s.PairwiseDisjoint f :=
  hc.pairwise_iUnion₂