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Theorems · Theorem · combinatorics

Finset.mem_powerset

∀ {α : Type u_1} {s t : Finset α}, s ∈ t.powerset ↔ s ⊆ t
Defined in
Mathlib.Data.Finset.Powerset
Cited by
26 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

Finset.powerset_card_disjiUnion · cited by 3Finset.powerset_card_disj…Finset.powerset_mono · cited by 3Finset.powerset_monosummable_finsetProd_of_summable_nonneg · cited by 3summable_finsetProd_of_su…Finset.sum_powerset_insert · cited by 2Finset.sum_powerset_insertFinset.pluennecke_ruzsa_inequality_pow_div_pow_mul · cited by 2Finset.pluennecke_ruzsa_i…Finset.ruzsa_covering_add · cited by 2Finset.ruzsa_covering_addFinset.ruzsa_triangle_inequality_add_add_add · cited by 2Finset.ruzsa_triangle_ine…Finset.ruzsa_triangle_inequality_mul_mul_mul · cited by 2Finset.ruzsa_triangle_ine…Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add · cited by 2Finset.pluennecke_ruzsa_i…Finset.sum_powerset_apply_card · cited by 1Finset.sum_powerset_apply…Nat.smoothNumbersUpTo_subset_image · cited by 1Nat.smoothNumbersUpTo_sub…Finset.shatters_iff · cited by 1Finset.shatters_iffUnconditionalSchauderBasis.exists_norm_proj_le · cited by 1UnconditionalSchauderBasi…Finset.prod_powerset_insert · cited by 1Finset.prod_powerset_inse…ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefree · cited by 1IsMultiplicative.prodPrim…Finset · cited by 13712FinsetMultiset · cited by 2627MultisetFinset.val · cited by 438Finset.valMultiset.Nodup · cited by 148Multiset.NodupFinset.powerset · cited by 93Finset.powersetMultiset.powerset · cited by 27Multiset.powersetFinset.casesOn · cited by 17Finset.casesOnFinset.mk.injEq · cited by 4mk.injEqFinset.mem_powersetCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.