Theorems · Theorem · combinatorics
Finset.insert_erase
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {a : α}, a ∈ s → insert a (s.erase a) = s- Defined in
- Mathlib.Data.Finset.Basic
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 56 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.
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
- Finset.erasestatement · cited by 455
Cited by65
Results whose statement or proof uses this declaration.
- Finset.add_sum_eraseproof · cited by 28
- Finset.mul_prod_eraseproof · cited by 23
- Finset.card_eq_succproof · cited by 7
- Finset.insert_erase_invOnproof · cited by 6
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Finset.fold_insert_idemproof · cited by 5
- Ideal.subset_union_primeproof · cited by 4
- MvPowerSeries.mul_invOfUnitproof · cited by 4
- Finset.induction_on_maxproof · cited by 4
- IsLocalization.exist_integer_multiplesproof · cited by 4
- Finpartition.equitabilise_auxproof · cited by 3
- AddMonoidHom.noncommPiCoprod_singleproof · cited by 3