Theorems · Theorem · order theory
Localization.mk_le_mk
∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelMonoid α] {s : Submonoid α}
{a₁ b₁ : α} {a₂ b₂ : ↥s}, Localization.mk a₁ a₂ ≤ Localization.mk b₁ b₂ ↔ ↑b₂ * a₁ ≤ ↑a₂ * b₁- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- IsOrderedCancelMonoidstatement and proof · cited by 65
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