Theorems · Theorem · order theory
isGLB_Ici
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsGLB (Set.Ici a) a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 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.Icistatement · cited by 1,070
- IsGLBstatement · cited by 213
- IsLeast.isGLBproof · cited by 23
- isLeast_Iciproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- bddBelow_Iciproof · cited by 5
- Order.isGLB_Ioi_iff_isPredPrelimitproof · cited by 0
- lowerBounds_Iciproof · cited by 0