Theorems · Theorem · order theory
iSup_of_empty
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] [IsEmpty ι] (f : ι → α), iSup f = ⊥- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLatticeIsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- IsEmptystatement and proof · cited by 759
- sSup_emptyproof · cited by 19
- iSup_of_empty'proof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- Set.iUnion_of_emptyproof · cited by 68
- SupClosed.iSup_memproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_iSupproof · cited by 1
- LieModule.exists_nontrivial_weightSpace_of_isNilpotentproof · cited by 0
- IntermediateField.toSubalgebra_iSup_of_directedproof · cited by 0