Theorems · Theorem · order theory
upperBounds_lowerClosure
∀ {α : Type u_1} [inst : Preorder α] {s : Set α}, upperBounds ↑(lowerClosure s) = upperBounds s- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 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.
Cites10
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
- SetLike.coestatement and proof · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- LE.le.antisymmproof · cited by 507
- upperBoundsstatement and proof · cited by 263
- LowerSetstatement · cited by 230
- LE.le.trans'proof · cited by 140
- lowerClosurestatement and proof · cited by 83
- upperBounds_mono_setproof · cited by 13
- subset_lowerClosureproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- bddAbove_lowerClosureproof · cited by 3