Theorems · Theorem · order theory
iInf_eq_top
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {s : ι → α}, iInf s = ⊤ ↔ ∀ (i : ι), s i = ⊤- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 10 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.
- Top.topstatement · cited by 9,680
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- Set.forall_mem_rangeproof · cited by 135
- sInf_eq_topproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- ENNReal.mul_iInf'proof · cited by 3
- iInf_codisjoint_iffproof · cited by 2
- AddMonoid.minOrder_eq_topproof · cited by 1
- MeasureTheory.extend_topproof · cited by 1
- iInf₂_eq_topproof · cited by 1
- iInf_lt_topproof · cited by 1
- sInf_codisjoint_iffproof · cited by 1
- MeasureTheory.OuterMeasure.mkMetric'_isMetricproof · cited by 0
- AddMonoid.minOrder_eq_top_iffproof · cited by 0
- Set.iInter_eq_univproof · cited by 0