Theorems · Theorem · combinatorics
Finset.mem_of_mem_filter
∀ {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] {s : Finset α}, ∀ x ∈ Finset.filter p s, x ∈ s- Defined in
- Mathlib.Data.Finset.Filter
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 54 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 and proof · cited by 949
- Multiset.mem_of_mem_filterproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_memproof · cited by 3
- Nat.lt_of_mem_primesBelowproof · cited by 3
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsumproof · cited by 3
- Subgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- AddSubgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- Nat.smoothNumbers_eq_factoredNumbers_primesBelowproof · cited by 1
- Fin.card_filter_univ_succproof · cited by 1
- StrictConvexOn.map_sum_eq_iff_of_nonnegproof · cited by 1
- Real.geom_mean_eq_arith_mean_weighted_iff_of_nonnegproof · cited by 1
- Real.geom_mean_eq_arith_mean_weighted_iff_of_nonneg'proof · cited by 1
- StrictConvexOn.map_sum_lt_iff_of_nonneg'proof · cited by 1