Theorems · Theorem · order theory
nsmul_nonpos
∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddLeftMono M] {a : M}, a ≤ 0 → ∀ (n : ℕ), n • a ≤ 0Alias of Left.nsmul_nonpos.
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- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddMonoidPreorderAddLeftMono
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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_nonposproof · cited by 2
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