Theorems · Theorem · order theory
sSup_range
∀ {α : Type u_1} {ι : Sort u_4} [inst : SupSet α] {f : ι → α}, sSup (Set.range f) = iSup f- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- SupSet
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
- iSupstatement · cited by 2,415
- SupSet.sSupstatement · cited by 954
- SupSetstatement and proof · cited by 154
Cited by20
Results whose statement or proof uses this declaration.
- GaloisConnection.l_iSupproof · cited by 78
- Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndexproof · cited by 5
- Seminorm.coe_iSup_eqproof · cited by 3
- ConvexOn.sSup_of_nat_affine_eqproof · cited by 2
- Dense.ciSupproof · cited by 2
- Ordinal.sSup_add_one_lt_of_lt_cofproof · cited by 2
- Filter.limsup_top_eq_ciSupproof · cited by 1
- Filter.limsup_top_eq_iSupproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_iSupproof · cited by 1
- Real.tendsto_atTop_csSup_of_monotoneOn_bddAbove_nat_Iciproof · cited by 1
- Ordinal.mul_iSupproof · cited by 1
- Set.exists_seq_iSup_eq_top_iff_countableproof · cited by 1