Theorems · Theorem · order theory
sInf_range
∀ {α : Type u_1} {ι : Sort u_4} [inst : InfSet α] {f : ι → α}, sInf (Set.range f) = iInf f- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- InfSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement · cited by 4,705
- iInfstatement · cited by 1,690
- InfSet.sInfstatement · cited by 935
- InfSetstatement and proof · cited by 145
Cited by17
Results whose statement or proof uses this declaration.
- GaloisConnection.u_iInfproof · cited by 40
- topologicalAddGroup_iInfproof · cited by 5
- Real.tendsto_atTop_csInf_of_antitoneOn_bddBelow_nat_Iciproof · cited by 3
- isUniformAddGroup_iInfproof · cited by 2
- continuousAdd_iInfproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_iSupproof · cited by 1
- Filter.liminf_top_eq_ciInfproof · cited by 1
- Filter.liminf_top_eq_iInfproof · cited by 1
- continuousInv_iInfproof · cited by 1
- isUniformGroup_iInfproof · cited by 1
- continuousMul_iInfproof · cited by 1
- topologicalGroup_iInfproof · cited by 1