Theorems · Theorem · order theory
upperBounds_mono_of_isCofinalFor
∀ {α : Type u_1} [inst : Preorder α] {s t : Set α}, IsCofinalFor s t → upperBounds t ⊆ upperBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 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.
Cites5
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
- LE.le.transproof · cited by 3,151
- upperBoundsstatement and proof · cited by 263
- IsCofinalForstatement and proof · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- IsLUB.of_isCofinalForproof · cited by 2
- Monotone.upperBounds_image_of_directedOn_prodproof · cited by 1
- sSup_le_sSup_of_isCofinalForproof · cited by 0