Theorems · Theorem · order theory
iSup_eq_bot
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {s : ι → α}, iSup s = ⊥ ↔ ∀ (i : ι), s i = ⊥- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
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.
- Bot.botstatement · cited by 4,720
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Set.forall_mem_rangeproof · cited by 135
- sSup_eq_botproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- ENNReal.iSup_eq_zeroproof · cited by 3
- sSupIndep_iff_finiteproof · cited by 1
- ENat.iSup_eq_zeroproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.multiplicity_iSupproof · cited by 0
- Set.iUnion_eq_emptyproof · cited by 0