Theorems · Theorem · order theory
smul_upperBounds_subset_upperBounds_smul_of_nonneg
∀ {α : Type u_1} {β : Type u_2} [inst : SMul α β] [inst_1 : Preorder α] [inst_2 : Preorder β] [inst_3 : Zero α]
[PosSMulMono α β] {a : α} {s : Set β}, 0 ≤ a → a • upperBounds s ⊆ upperBounds (a • s)- Defined in
- Mathlib.Algebra.Order.Module.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
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 and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.smulSetstatement · cited by 608
- upperBoundsstatement · cited by 263
- PosSMulMonostatement and proof · cited by 188
- monotone_smul_left_of_nonnegproof · cited by 9
- Monotone.image_upperBounds_subset_upperBounds_imageproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.