Theorems · Theorem · order theory
Set.Finite.subset
∀ {α : Type u} {s : Set α}, s.Finite → ∀ {t : Set α}, t ⊆ s → t.Finite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 285 results in Mathlib
- Foundations
- Depth 64 from the axioms, rests on 1,050 definitions · 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.Elemproof · cited by 7,166
- Finiteproof · cited by 3,029
- Set.Finitestatement and proof · cited by 1,814
- Set.Finite.to_subtypeproof · cited by 44
- Finite.Set.subsetproof · cited by 1
Cited by286
Results whose statement or proof uses this declaration.
- Filter.cofiniteproof · cited by 251
- Set.Finite.inter_of_leftproof · cited by 31
- Set.Infinite.monoproof · cited by 25
- Set.Finite.preimageproof · cited by 16
- Set.Finite.sdiffproof · cited by 15
- Set.ncard_le_ncardproof · cited by 15
- LocallyFinite.subsetproof · cited by 14
- Matroid.IsRkFinite.subsetproof · cited by 10
- Set.eq_of_subset_of_ncard_leproof · cited by 10
- LocallyFinite.point_finiteproof · cited by 9
- memℓp_genproof · cited by 8
- Set.Finite.of_injOnproof · cited by 7
Showing the 200 most cited of 286.