Theorems · Theorem · combinatorics
Finset.mem_insert_of_mem
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {a b : α}, a ∈ s → a ∈ insert b s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 109 results in Mathlib
- Foundations
- Depth 54 from the axioms, rests on 815 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- Multiset.mem_ndinsert_of_memproof · cited by 2
Cited by110
Results whose statement or proof uses this declaration.
- Finset.subset_insertproof · cited by 36
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
- affineIndependent_iff_linearIndependent_vsubproof · cited by 11
- Finset.noncommProd_insert_of_notMemstatement and proof · cited by 8
- MeromorphicAt.prodproof · cited by 7
- ProbabilityTheory.Kernel.iIndepFun.indepFun_prodMkproof · cited by 7
- Affine.Simplex.sum_pointsWithCircumcenterproof · cited by 7
- MonovaryOn.sum_smul_comp_perm_le_sum_smulproof · cited by 7
- Finset.card_dvd_card_image₂_rightproof · cited by 6
- ProbabilityTheory.Kernel.iIndepFun.indepFun_prodMk_prodMkproof · cited by 6
- Polynomial.support_trinomial_subsetproof · cited by 5
- MeasureTheory.IsSetRing.biUnion_memproof · cited by 5