Theorems · Theorem · combinatorics
Finset.filter_subset_filter
∀ {α : Type u_1} (p : α → Prop) [inst : DecidablePred p] {s t : Finset α}, s ⊆ t → Finset.filter p s ⊆ Finset.filter p t- Defined in
- Mathlib.Data.Finset.Filter
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 55 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
- Finset.mem_filterproof · cited by 185
Cited by11
Results whose statement or proof uses this declaration.
- Finpartition.equitabilise_auxproof · cited by 3
- BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleOproof · cited by 2
- Finset.disjSups_subsetproof · cited by 2
- Finset.addEnergy_monoproof · cited by 2
- Finset.mulEnergy_monoproof · cited by 2
- Nat.Ico_filter_coprime_leproof · cited by 1
- Nat.properDivisors_subset_divisorsproof · cited by 1
- primorial_monoproof · cited by 1
- Chebyshev.theta_monoproof · cited by 0
- Finset.monotone_filter_leftproof · cited by 0
- primorial_dvd_primorialproof · cited by 0