Theorems · Theorem · order theory
sInf_eq_top
∀ {α : Type u_1} [inst : CompleteLattice α] {s : Set α}, sInf s = ⊤ ↔ ∀ a ∈ s, a = ⊤- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfstatement and proof · cited by 935
- top_le_iffproof · cited by 175
- sInf_leproof · cited by 110
- top_uniqueproof · cited by 102
- le_sInfproof · cited by 51
Cited by5
Results whose statement or proof uses this declaration.
- iInf_eq_topproof · cited by 10
- eq_singleton_top_of_sInf_eq_top_of_nonemptyproof · cited by 0
- Set.sInter_eq_univproof · cited by 0
- sInf_eq_top'proof · cited by 0
- MeasureTheory.hittingBtwn_eq_sInfproof · cited by 0