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Theorems · Theorem · order theory

Finset.mem_sup

∀ {α : Type u_2} {ι : Type u_5} [inst : DecidableEq α] {s : Finset ι} {f : ι → Finset α} {a : α},
  a ∈ s.sup f ↔ ∃ i ∈ s, a ∈ f i
Defined in
Mathlib.Data.Finset.Lattice.Fold
Cited by
4 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Finset.mem_sym_iff · cited by 9Finset.mem_sym_iffFinset.sup_eq_biUnion · cited by 7Finset.sup_eq_biUnionFinpartition.exists_mem · cited by 3Finpartition.exists_memFinset.sup_singleton_apply · cited by 1Finset.sup_singleton_applyFinset · cited by 13712FinsetFinset.sup · cited by 530Finset.supFinset.cons_induction · cited by 85Finset.cons_inductionFinset.sup_empty · cited by 72Finset.sup_emptyFinset.sup_cons · cited by 30Finset.sup_consFinset.mem_supCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.