Theorems · Theorem · combinatorics
Finset.toFinset_coe
∀ {α : Type u_1} (s : Finset α) [inst : Fintype ↑↑s], (↑s).toFinset = s- Defined in
- Mathlib.Data.Fintype.Sets
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 58 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.extproof · cited by 565
- Set.toFinsetstatement · cited by 217
- Set.mem_toFinsetproof · cited by 47
Cited by16
Results whose statement or proof uses this declaration.
- Summable.hasSumproof · cited by 184
- Multipliable.hasProdproof · cited by 88
- Set.encard_coe_eq_coe_finsetCardproof · cited by 6
- Finset.finite_toSet_toFinsetproof · cited by 2
- Finset.coe_infsepproof · cited by 2
- ConjRootClass.aroots_minpoly_eq_carrier_valproof · cited by 1
- finrank_span_finset_eq_cardproof · cited by 1
- Finset.card_mul_finset_lt_twoproof · cited by 1
- finrank_span_finset_le_cardproof · cited by 1
- SimpleGraph.set_walk_length_toFinset_eqproof · cited by 0
- Finset.existsproof · cited by 0
- Finset.forallproof · cited by 0