Theorems · Theorem · order theory
isLUB_singleton
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsLUB {a} a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- IsLUBstatement · cited by 280
- IsGreatest.isLUBproof · cited by 25
- isGreatest_singletonproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- sSup_singletonproof · cited by 14
- isLUB_pairproof · cited by 5
- upperBounds_singletonproof · cited by 4
- IsLUB.insertproof · cited by 4
- IsLUB.mul_leftproof · cited by 2
- bddAbove_singletonproof · cited by 2
- PartialOrder.dirSupClosed_singletonproof · cited by 1
- DirSupClosed.mem_imp_of_antisymmRelproof · cited by 1
- ScottContinuous.prodproof · cited by 0
- CountableSupClosed.singletonproof · cited by 0