Theorems · Theorem · order theory
NoBotOrder.lowerBounds_univ
∀ {α : Type u_1} [inst : Preorder α] [NoBotOrder α], lowerBounds Set.univ = ∅- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderNoBotOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.univstatement and proof · cited by 3,945
- Set.mem_univproof · cited by 416
- lowerBoundsstatement and proof · cited by 212
- NoBotOrderstatement and proof · cited by 43
- Set.eq_empty_of_subset_emptyproof · cited by 15
- not_isBotproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- not_bddBelow_univproof · cited by 0