Theorems · Theorem · order theory
isLUB_empty_iff
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsLUB ∅ a ↔ IsBot a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 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 · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- IsLUBstatement · cited by 280
- IsLeastproof · cited by 122
- IsBotstatement and proof · cited by 77
- upperBounds_emptyproof · cited by 3
- isLeast_univ_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isLUB_emptyproof · cited by 1