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Theorems · Theorem · order theory

Left.nsmul_nonpos

∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddLeftMono M] {a : M}, a ≤ 0 → ∀ (n : ℕ), n • a ≤ 0
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Pow
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
AddMonoidPreorderAddLeftMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Left.nsmul_neg · cited by 1Left.nsmul_negnsmul_nonpos · cited by 0nsmul_nonposPreorder · cited by 7952PreorderAddMonoid · cited by 2864AddMonoidAddLeftMono · cited by 687AddLeftMonoLeft.nsmul_nonneg · cited by 2Left.nsmul_nonnegLeft.nsmul_nonposCITED BYCITES

Cites4

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Cited by2

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