Theorems · Theorem · order theory
OrderTop.bddAbove
∀ {α : Type u_1} [inst : Preorder α] [OrderTop α] (s : Set α), BddAbove sWhen there is a global maximum, every set is bounded above.
- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by16
Results whose statement or proof uses this declaration.
- tendsto_atTop_iSupproof · cited by 9
- Order.krullDim_eq_iSup_lengthproof · cited by 5
- Order.krullDim_eq_iSup_height_of_nonemptyproof · cited by 4
- MonotoneOn.map_sSup_of_continuousWithinAtproof · cited by 3
- iSup_partialSups_eqproof · cited by 3
- Order.krullDim_eq_iSup_heightproof · cited by 3
- Monotone.iSup_comp_tendsto_atTopproof · cited by 2
- tendsto_atBot_iSupproof · cited by 1
- Antitone.iSup_comp_tendsto_atBotproof · cited by 1
- Order.krullDim_eq_iSup_coheightproof · cited by 1
- csSup_eq_top_of_top_memproof · cited by 1
- MeasureTheory.Measure.haveLebesgueDecomposition_of_finiteMeasureproof · cited by 0