Theorems · Theorem · order theory
DedekindCut.upperBounds_left
∀ {α : Type u_1} [inst : Preorder α] (A : DedekindCut α), upperBounds A.left = A.right- Defined in
- Mathlib.Order.Completion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- upperBoundsstatement · cited by 263
- DedekindCutstatement and proof · cited by 27
- DedekindCut.leftstatement · cited by 16
- DedekindCut.rightstatement · cited by 12
- Concept.upperPolar_extentproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- DedekindCut.principal_sSup_leftproof · cited by 0