Theorems · Theorem · combinatorics
Finset.filter_union_filter_not_eq
∀ {α : Type u_1} (p : α → Prop) [inst : DecidablePred p] [inst_1 : DecidableEq α] [inst_2 : (x : α) → Decidable ¬p x]
(s : Finset α), Finset.filter p s ∪ {a ∈ s | ¬p a} = s- Defined in
- Mathlib.Data.Finset.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- codisjoint_hnot_rightproof · cited by 7
- Finset.filter_union_filter_of_codisjointproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- Finset.sum_filter_add_sum_filter_notproof · cited by 20
- Finset.card_filter_add_card_filter_notproof · cited by 7
- Finset.prod_filter_mul_prod_filter_notproof · cited by 6
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Finset.sum_le_sum_of_ne_zeroproof · cited by 2
- Subgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- AddSubgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- Rel.card_interedges_add_card_interedges_complproof · cited by 1
- UV.card_compressionproof · cited by 1
- SimpleGraph.card_interedges_add_card_interedges_complproof · cited by 1
- Finset.gcd_eq_gcd_filter_ne_zeroproof · cited by 0