Theorems · Theorem · order theory
upperBounds_empty
∀ {α : Type u_1} [inst : Preorder α], upperBounds ∅ = Set.univ- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- 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
- Set.ofPredproof · cited by 6,101
- Set.univstatement and proof · cited by 3,945
- upperBoundsstatement · cited by 263
Cited by3
Results whose statement or proof uses this declaration.
- bddAbove_emptyproof · cited by 3
- isLUB_empty_iffproof · cited by 1
- IsLUB.nonemptyproof · cited by 0