Theorems · Theorem · order theory
upperBounds_mono
∀ {α : Type u_1} [inst : Preorder α] ⦃s t : Set α⦄, s ⊆ t → ∀ ⦃a b : α⦄, a ≤ b → a ∈ upperBounds t → b ∈ upperBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 1 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.
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
- upperBoundsstatement and proof · cited by 263
- upperBounds_mono_setproof · cited by 13
- upperBounds_mono_memproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Dense.upperBounds_imageproof · cited by 2