Theorems · Theorem · combinatorics
Finset.mem_insert_self
∀ {α : Type u_1} [inst : DecidableEq α] (a : α) (s : Finset α), a ∈ insert a s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 128 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.
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.valproof · cited by 438
- Multiset.mem_ndinsert_selfproof · cited by 3
Cited by130
Results whose statement or proof uses this declaration.
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
- Finset.insert_nonemptyproof · 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
- Finsupp.induction_on_maxproof · cited by 6
- ProbabilityTheory.Kernel.iIndepFun.indepFun_prodMk_prodMkproof · cited by 6
- MeasureTheory.IsSetRing.biUnion_memproof · cited by 5
- collapse_eqproof · cited by 5
- Polynomial.support_trinomial_subsetproof · cited by 5