Theorems · Theorem · order theory
IsChain.pairwise_sUnion
∀ {α : Type u_1} {c : Set (Set α)} {r : α → α → Prop},
IsChain (fun x1 x2 => x1 ⊆ x2) c → ((⋃₀ c).Pairwise r ↔ ∀ s ∈ c, s.Pairwise r)- Defined in
- Mathlib.Data.Set.Pairwise.Chain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.sUnionstatement · cited by 392
- Set.Pairwisestatement · cited by 321
- IsChainstatement and proof · cited by 158
- IsChain.directedOnproof · cited by 28
- Set.pairwise_sUnionproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsChain.pairwiseDisjoint_sUnionproof · cited by 0