Theorems · Theorem · order theory
Finset.sup_singleton
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {f : β → α} {b : β}, {b}.sup f = f b- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeSupOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- Multiset.sup_singletonproof · cited by 1
Cited by42
Results whose statement or proof uses this declaration.
- Polynomial.degree_Cproof · cited by 20
- MonomialOrder.degree_monomialproof · cited by 12
- Finset.SupIndep.pairwiseDisjointproof · cited by 7
- CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSupproof · cited by 4
- WithSeminorms.congr_equivproof · cited by 4
- WithSeminorms.isVonNBounded_iff_seminorm_boundedproof · cited by 4
- Finset.SupIndep.biUnionproof · cited by 4
- Finset.supIndep_pairproof · cited by 3
- MonomialOrder.degree_monomial_leproof · cited by 3
- iSup_fin_threeproof · cited by 3
- Module.Dual.exists_continuous_extension_of_le_seminormproof · cited by 2
- Topology.RelCWComplex.cellFrontier_one_eqproof · cited by 2