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Theorems · Theorem · order theory

zsmul_pos

∀ {G : Type u_2} [inst : SubNegMonoid G] [inst_1 : Preorder G] [AddLeftMono G] {x : G},
  0 < x → ∀ {n : ℤ}, 0 < n → 0 < n • x
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Pow
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext
Assumes
SubNegMonoidPreorderAddLeftMono
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Around this declaration

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

zsmul_strictMono_right · cited by 3zsmul_strictMono_rightPreorder · cited by 7952PreorderLT.lt.ne' · cited by 1417lt.ne'AddLeftMono · cited by 687AddLeftMononatCast_zsmul · cited by 118natCast_zsmulSubNegMonoid · cited by 79SubNegMonoidnsmul_pos · cited by 1nsmul_poszsmul_posCITED BYCITES

Cites6

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Cited by1

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