Theorems · Theorem · order theory
lowerClosure_empty
∀ {α : Type u_1} [inst : Preorder α], lowerClosure ∅ = ⊥- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, 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
- Bot.botstatement · cited by 4,720
- LowerSetstatement · cited by 230
- lowerClosurestatement · cited by 83
- lowerClosure_eq_bot_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finset.truncatedSup_emptyproof · cited by 0