Theorems · Theorem · combinatorics
Finset.disjoint_filter_filter_not
∀ {α : Type u_1} (s t : Finset α) (p : α → Prop) [inst : DecidablePred p] [inst_1 : (x : α) → Decidable ¬p x],
Disjoint (Finset.filter p s) ({a ∈ t | ¬p a})- Defined in
- Mathlib.Data.Finset.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePredDecidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Disjointstatement · cited by 2,201
- Finset.filterstatement · cited by 949
- disjoint_compl_rightproof · cited by 47
- Finset.disjoint_filter_filter'proof · cited by 3
Cited by6
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
- UV.card_compressionproof · cited by 1
- Finset.dens_filter_add_dens_filter_not_eq_densproof · cited by 0
- Down.card_compressionproof · cited by 0