Theorems · Theorem · order theory
upperBounds_insert
∀ {α : Type u_1} [inst : Preorder α] (a : α) (s : Set α), upperBounds (insert a s) = Set.Ici a ∩ upperBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Icistatement and proof · cited by 1,070
- upperBoundsstatement and proof · cited by 263
- Set.insert_eqproof · cited by 47
- upperBounds_singletonproof · cited by 4
- upperBounds_unionproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- ScottContinuousOn.monotoneproof · cited by 5
- LeftOrdContinuous.monoproof · cited by 1
- eVariationOn.union'proof · cited by 0