Theorems · Theorem · order theory
Monotone.le_map_iSup
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : CompleteLattice α] {s : ι → α} [inst_1 : CompleteLattice β]
{f : α → β}, Monotone f → ⨆ i, f (s i) ≤ f (iSup s)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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.
- iSupstatement and proof · cited by 2,415
- Monotonestatement and proof · cited by 1,397
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
Cited by8
Results whose statement or proof uses this declaration.
- Filter.ker_iSupproof · cited by 2
- LocallyFinite.nhdsWithin_iUnionproof · cited by 2
- MeasureTheory.iSup_lintegral_leproof · cited by 1
- AddSubgroup.iSup_comap_leproof · cited by 0
- Sublattice.le_comap_iSupproof · cited by 0
- BooleanSubalgebra.le_comap_iSupproof · cited by 0
- Subgroup.iSup_comap_leproof · cited by 0
- Antitone.le_map_iInfproof · cited by 0