Theorems · Theorem · order theory
upperBounds_singleton
∀ {α : Type u_1} [inst : Preorder α] {a : α}, upperBounds {a} = Set.Ici a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Icistatement · cited by 1,070
- upperBoundsstatement · cited by 263
- IsLUB.upperBounds_eqproof · cited by 10
- isLUB_singletonproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- ScottContinuousOn.monotoneproof · cited by 5
- upperBounds_insertproof · cited by 3
- LeftOrdContinuous.monoproof · cited by 1
- isLUB_iUnion_iff_of_isLUBproof · cited by 1