Theorems · Theorem · order theory
upperBounds_mono_mem
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} ⦃a b : α⦄, a ≤ b → a ∈ upperBounds s → b ∈ upperBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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_transproof · cited by 985
- upperBoundsstatement and proof · cited by 263
Cited by4
Results whose statement or proof uses this declaration.
- IsLUB.upperBounds_eqproof · cited by 10
- BddAbove.unionproof · cited by 2
- upperBounds_monoproof · cited by 1
- eVariationOn.union'proof · cited by 0