Theorems · Theorem · combinatorics
Finset.card_singleton
∀ {α : Type u_1} (a : α), {a}.card = 1- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 144 results in Mathlib
- Foundations
- Depth 25 from the axioms, rests on 133 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Finset.cardstatement · cited by 2,327
- Multiset.card_singletonproof · cited by 17
Cited by145
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.count_singleton'proof · cited by 10
- Matrix.vecMulVec_eqproof · cited by 7
- Orientation.eq_or_eq_neg_of_isEmptyproof · cited by 6
- groupHomology.comp_d₁₀_eqproof · cited by 6
- Finset.sum_update_of_memproof · cited by 5
- MeasureTheory.Measure.hausdorffMeasure_zero_singletonproof · cited by 5
- Finset.prod_update_of_memproof · cited by 5
- Polynomial.natSepDegree_X_sub_Cproof · cited by 4
- Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsubproof · cited by 4
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- MultilinearMap.norm_image_sub_le_of_boundproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3