Theorems · Theorem · order theory
Finset.sup_union
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s₁ s₂ : Finset β} {f : β → α}
[inst_2 : DecidableEq β], (s₁ ∪ s₂).sup f = s₁.sup f ⊔ s₂.sup f- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 13,712
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- eq_of_forall_ge_iffproof · cited by 96
Cited by9
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.sup_support_coeff_add_leproof · cited by 5
- CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSupproof · cited by 4
- Finset.SupIndep.biUnionproof · cited by 4
- BooleanSubalgebra.mem_closure_iff_sup_sdiffproof · cited by 1
- BoxIntegral.TaggedPrepartition.distortion_disjUnionproof · cited by 1
- exists_supIrred_decompositionproof · cited by 1
- NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlaceproof · cited by 1
- BoxIntegral.Prepartition.distortion_disjUnionproof · cited by 1
- Finset.max_unionproof · cited by 0