Theorems · Theorem · order theory
BddAbove.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}, BddAbove s → 0 ≤ a → BddAbove (a • s)- Defined in
- Mathlib.Algebra.Order.Module.Pointwise
- Cited by
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- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
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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
- BddAbovestatement and proof · cited by 620
- Set.smulSetstatement · cited by 608
- PosSMulMonostatement and proof · cited by 188
- monotone_smul_left_of_nonnegproof · cited by 9
- Monotone.map_bddAboveproof · cited by 9
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