Theorems · Theorem · combinatorics
Finset.filter_insert
∀ {α : Type u_1} (p : α → Prop) [inst : DecidablePred p] [inst_1 : DecidableEq α] (a : α) (s : Finset α),
Finset.filter p (insert a s) = if p a then insert a (Finset.filter p s) else Finset.filter p s- Defined in
- Mathlib.Data.Finset.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePredDecidableEq
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.filterstatement · cited by 949
Cited by14
Results whose statement or proof uses this declaration.
- Finpartition.equitabilise_auxproof · cited by 3
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsumproof · cited by 3
- Nat.insert_self_properDivisorsproof · cited by 3
- schnirelmannDensity_le_of_notMemproof · cited by 2
- Finset.prod_add_orderedproof · cited by 2
- AffineBasis.surjective_coordproof · cited by 1
- Nat.card_multiples'proof · cited by 1
- Nat.primesBelow_succproof · cited by 1
- Nat.totient_eq_iff_primeproof · cited by 1
- Finset.fold_ite'proof · cited by 1
- primorial_succproof · cited by 1
- Finset.gcd_eq_gcd_filter_ne_zeroproof · cited by 0