Theorems · Theorem · order theory
Set.Finite.mem_toFinset
∀ {α : Type u} {s : Set α} {a : α} (hs : s.Finite), a ∈ hs.toFinset ↔ a ∈ s- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 74 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finsetstatement · cited by 13,712
- Set.Finitestatement and proof · cited by 1,814
- Set.Finite.toFinsetstatement · cited by 351
- Set.mem_toFinsetproof · cited by 47
Cited by74
Results whose statement or proof uses this declaration.
- Summable.hasSumproof · cited by 184
- MeasureTheory.SimpleFunc.mem_rangeproof · cited by 13
- Finset.mem_preimageproof · cited by 12
- summable_of_hasFiniteSupportproof · cited by 12
- MeasureTheory.measure_biUnion_lt_topproof · cited by 8
- finprod_eq_prod_of_mulSupport_toFinset_subsetproof · cited by 6
- Set.exists_max_imageproof · cited by 5
- Finset.mem_vaddAntidiagonalproof · cited by 5
- finsum_eq_sum_of_support_toFinset_subsetproof · cited by 5
- finsum_eq_sum_plift_of_support_subsetproof · cited by 5
- Finset.mem_antidiagonalproof · cited by 5
- finprod_eq_prod_plift_of_mulSupport_subsetproof · cited by 5