Theorems · Theorem · combinatorics
Fintype.card_coe
∀ {α : Type u_1} (s : Finset α) [inst : Fintype ↥s], Fintype.card ↥s = s.card- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 61 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.
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- Fintype.card_of_finset'proof · cited by 13
Cited by72
Results whose statement or proof uses this declaration.
- Cardinal.lt_aleph0proof · cited by 19
- Equiv.Perm.IsCycle.orderOfproof · cited by 14
- Cardinal.mk_coe_finsetproof · cited by 5
- Polynomial.natSepDegree_expandproof · cited by 4
- Finset.card_eq_of_equivproof · cited by 3
- Ideal.height_le_card_of_mem_minimalPrimes_span_finsetproof · cited by 3
- Polynomial.card_rootSet_eq_natDegreeproof · cited by 3
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Nat.card_eq_finsetCardproof · cited by 3
- Convex.helly_theorem'proof · cited by 3
- Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zeroproof · cited by 2