Theorems · Theorem · order theory
Set.infinite_iUnion
∀ {α : Type u} {ι : Type u_1} [Infinite ι] {s : ι → Set α}, Function.Injective s → (⋃ i, s i).Infinite- Defined in
- Mathlib.Data.Set.Finite.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.iUnionstatement and proof · cited by 2,483
- Set.Finiteproof · cited by 1,814
- Infinitestatement and proof · cited by 352
- Set.Infinitestatement · cited by 263
- Set.subset_iUnionproof · cited by 81
- not_injective_infinite_finiteproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- exists_seq_infinite_isOpen_pairwise_disjointproof · cited by 1
- Set.Infinite.sUnionproof · cited by 0
- Set.Infinite.biUnionproof · cited by 0