Theorems · Theorem · order theory
isLUB_Iic
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsLUB (Set.Iic a) a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- 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.
- Preorderstatement and proof · cited by 7,952
- Set.Iicstatement · cited by 1,111
- IsLUBstatement · cited by 280
- IsGreatest.isLUBproof · cited by 25
- isGreatest_Iicproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- bddAbove_Iicproof · cited by 4
- Order.isLUB_Iio_iff_isSuccPrelimitproof · cited by 0
- upperBounds_Iicproof · cited by 0