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Theorems · Theorem · combinatorics

Finset.filter_empty

∀ {α : Type u_1} (p : α → Prop) [inst : DecidablePred p], Finset.filter p ∅ = ∅
Defined in
Mathlib.Data.Finset.Filter
Cited by
23 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidablePred
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

primitiveRoots_zero · cited by 5primitiveRoots_zeroFinpartition.equitabilise_aux · cited by 3Finpartition.equitabilise…Nat.properDivisors_one · cited by 2Nat.properDivisors_oneRel.interedges_empty_left · cited by 2Rel.interedges_empty_leftQuadraticMap.map_sum · cited by 2QuadraticMap.map_sumFinset.prod_add_ordered · cited by 2Finset.prod_add_orderedPairReduction.card_pairSetSeq_le_logSizeRadius_mul · cited by 1PairReduction.card_pairSe…Finset.addEnergy_empty_left · cited by 1Finset.addEnergy_empty_le…Finset.addEnergy_empty_right · cited by 1Finset.addEnergy_empty_ri…Finset.fold_ite' · cited by 1Finset.fold_ite'Finpartition.isUniformOfEmpty · cited by 1Finpartition.isUniformOfE…Behrend.sphere_zero_right · cited by 1Behrend.sphere_zero_rightschnirelmannDensity_mul_le_card_filter · cited by 1schnirelmannDensity_mul_l…Finset.mulEnergy_empty_left · cited by 1Finset.mulEnergy_empty_le…Finset.mulEnergy_empty_right · cited by 1Finset.mulEnergy_empty_ri…Finset · cited by 13712FinsetFinset.filter · cited by 949Finset.filterFinset.filter_subset · cited by 55Finset.filter_subsetFinset.subset_empty · cited by 4Finset.subset_emptyFinset.filter_emptyCITED BYCITES

Cites4

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Cited by23

Results whose statement or proof uses this declaration.