Theorems · Theorem · order theory
IsGreatest.nonempty
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a : α}, IsGreatest s a → s.Nonempty- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptystatement · cited by 2,627
- IsGreateststatement and proof · cited by 112
Cited by2
Results whose statement or proof uses this declaration.
- IsGreatest.csSup_eqproof · cited by 9
- MonotoneOn.exists_monotone_extensionproof · cited by 2