Theorems · Theorem · order theory
nsmul_nonneg
∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddLeftMono M] {a : M}, 0 ≤ a → ∀ (n : ℕ), 0 ≤ n • aAlias of Left.nsmul_nonneg.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- AddMonoidPreorderAddLeftMono
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.
- Preorderstatement · cited by 7,952
- AddMonoidstatement · cited by 2,864
- AddLeftMonostatement · cited by 687
- Left.nsmul_nonnegproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- abs_nsmulproof · cited by 3
- zsmul_nonnegproof · cited by 3
- AddSubgroup.exists_isLeast_posproof · cited by 2
- nsmul_nonneg_iffproof · cited by 2
- Finsupp.le_weight_of_ne_zeroproof · cited by 1
- ArchimedeanClass.mk_le_mk_iff_denselyOrderedproof · cited by 1
- Function.locallyFinsuppWithin.nsmul_negPartproof · cited by 1
- Function.locallyFinsuppWithin.nsmul_posPartproof · cited by 1
- Nonneg.nsmul_mkstatement · cited by 0