Theorems · Theorem · combinatorics
Set.mem_toFinset
∀ {α : Type u_1} {s : Set α} [inst : Fintype ↑s] {a : α}, a ∈ s.toFinset ↔ a ∈ s- Defined in
- Mathlib.Data.Fintype.Sets
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.toFinsetstatement · cited by 217
Cited by48
Results whose statement or proof uses this declaration.
- Set.Finite.mem_toFinsetproof · cited by 74
- Set.coe_toFinsetproof · cited by 51
- Finset.toFinset_coeproof · cited by 16
- Matrix.det_fromBlocks_zero₂₁proof · cited by 10
- SimpleGraph.mem_edgeFinsetproof · cited by 6
- SimpleGraph.mem_neighborFinsetproof · cited by 6
- MDifferentiableWithinAt.sum_section_of_locallyFiniteproof · cited by 3
- Configuration.HasLines.lineCount_eq_pointCountproof · cited by 3
- ContMDiffWithinAt.sum_section_of_locallyFiniteproof · cited by 3
- Nat.card_eq_card_toFinsetproof · cited by 2
- IsCyclic.card_pow_eq_one_leproof · cited by 2
- Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_invproof · cited by 2