Theorems · Theorem · order theory
bddBelow_smul_iff_of_pos
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : GroupWithZero α] [inst_3 : Zero β]
[inst_4 : MulActionWithZero α β] [PosSMulMono α β] [PosSMulReflectLE α β] {s : Set β} {a : α},
0 < a → (BddBelow (a • s) ↔ BddBelow s)- Defined in
- Mathlib.Algebra.Order.Module.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- GroupWithZerostatement and proof · cited by 691
- Set.smulSetstatement · cited by 608
- BddBelowstatement · cited by 401
- PosSMulMonostatement and proof · cited by 188
- MulActionWithZerostatement and proof · cited by 79
- PosSMulReflectLEstatement and proof · cited by 51
- OrderIso.smulRightproof · cited by 8
- OrderIso.bddBelow_imageproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Real.sInf_smul_of_nonnegproof · cited by 3