Theorems · Theorem · order theory
Finset.inter_singleton_of_mem
∀ {α : Type u_1} [inst : DecidableEq α] {a : α} {s : Finset α}, a ∈ s → s ∩ {a} = {a}- Defined in
- Mathlib.Data.Finset.Lattice.Lemmas
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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 and proof · cited by 13,712
- Finset.inter_commproof · cited by 25
- Finset.singleton_inter_of_memproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Finset.prod_update_of_memproof · cited by 5
- Finset.sum_update_of_memproof · cited by 5
- Affine.Simplex.signedInfDist_affineCombinationproof · cited by 4
- Finset.sum_eq_add_sum_sdiff_singletonproof · cited by 3
- Finset.prod_eq_mul_prod_sdiff_singletonproof · cited by 2
- IsLowerSet.le_card_inter_finset'proof · cited by 1
- SSet.horn₂₂.sqproof · cited by 1
- Finset.inter_singletonproof · cited by 0