Theorems · Theorem · combinatorics
Finset.filter_true_of_mem
∀ {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] {s : Finset α}, (∀ x ∈ s, p x) → Finset.filter p s = sIf all elements of a Finset satisfy the predicate p, s.filter p is s.
- Defined in
- Mathlib.Data.Finset.Filter
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Finset.filter_eq_selfproof · cited by 5
Cited by24
Results whose statement or proof uses this declaration.
- SimpleGraph.cliqueSet_mapproof · cited by 3
- Finset.sum_subtype_of_memproof · cited by 3
- Finpartition.card_parts_equitabiliseproof · cited by 3
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsumproof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3
- Equiv.Perm.IsCycleOn.pow_apply_eqproof · cited by 2
- Multiset.toDFinsupp_supportproof · cited by 2
- Finset.prod_add_orderedproof · cited by 2
- AffineBasis.surjective_coordproof · cited by 1
- Finset.Ico_filter_le_of_le_leftproof · cited by 1
- schnirelmannDensity_eq_one_iffproof · cited by 1
- Finset.Ico_filter_lt_of_right_leproof · cited by 1