Sets · medium

Statement, exactly as the model and Lean see it

theorem lg_target {α : Type u_1} {c : Set (Set α)} {r : α → α → Prop} (hc : IsChain (fun x1 x2 => x1 ⊆ x2) c) : (⋃ s ∈ c, s).Pairwise r ↔ ∀ s ∈ c, s.Pairwise r := by

Mathlib declaration: IsChain.pairwise_iUnion₂
Held-out module: Mathlib.Data.Set.Pairwise.Chain
Banned modules (itself + downstream): 1
Reference proof premises (reachable / held-out): 3 / 0

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 pairwise_iUnion₂ : (⋃ s ∈ c, s).Pairwise r ↔ ∀ s ∈ c, s.Pairwise r :=
  pairwise_iUnion₂_iff hc.directedOn