Theorems · Theorem · order theory
isGLB_le_isLUB
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a b : α}, IsGLB s a → IsLUB s b → s.Nonempty → a ≤ b- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- 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 and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptystatement and proof · cited by 2,627
- IsLUBstatement and proof · cited by 280
- IsGLBstatement and proof · cited by 213
- lowerBounds_le_upperBoundsproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- csInf_le_csSupproof · cited by 2
- sInf_le_sSupproof · cited by 0
- DirectedOn.csInf_le_csSupproof · cited by 0