Theorems · Theorem · order theory
Set.finite_subset_iUnion
∀ {α : Type u} {s : Set α}, s.Finite → ∀ {ι : Type u_1} {t : ι → Set α}, s ⊆ ⋃ i, t i → ∃ I, I.Finite ∧ s ⊆ ⋃ i ∈ I, t i- Defined in
- Mathlib.Data.Set.Finite.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Finiteproof · cited by 3,029
- Set.iUnionstatement and proof · cited by 2,483
- Set.Finitestatement and proof · cited by 1,814
- Set.mem_iUnionproof · cited by 212
- Set.finite_rangeproof · cited by 58
- Set.Finite.to_subtypeproof · cited by 44
- Set.biUnion_rangeproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- linearIndepOn_iUnion_of_directedproof · cited by 4
- algebraicIndependent_iUnion_of_directedproof · cited by 1
- sSupIndep_iUnion_of_directedproof · cited by 1
- Set.eq_finite_iUnion_of_finite_subset_iUnionproof · cited by 1