Theorems · Theorem · combinatorics
Finset.erase_insert
∀ {α : Type u_1} [inst : DecidableEq α] {a : α} {s : Finset α}, a ∉ s → (insert a s).erase a = s- Defined in
- Mathlib.Data.Finset.Basic
- Cited by
- 21 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 by21
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_primeproof · cited by 7
- Finset.insert_erase_invOnproof · cited by 6
- Finsupp.induction_on_maxproof · cited by 6
- Nat.Prime.properDivisorsproof · cited by 4
- Finset.mem_memberSubfamilyproof · cited by 3
- DividedPowers.dpow_sum'proof · cited by 2
- Finset.induction_on_pi_of_choiceproof · cited by 2
- Down.mem_compressionproof · cited by 2
- DFinsupp.Lex.acc_of_singleproof · cited by 2
- HasMFDerivWithinAt.prodproof · cited by 2
- Finset.disjoint_of_erase_rightproof · cited by 1
- exists_sum_eq_one_iff_pairwise_coprimeproof · cited by 1