Theorems · Theorem · ring theory
OreLocalization.oreDiv_mul_oreDiv
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {r₁ r₂ : R} {s₁ s₂ : ↥S},
r₁ /ₒ s₁ * (r₂ /ₒ s₂) = OreLocalization.oreNum r₁ s₂ * r₂ /ₒ (OreLocalization.oreDenom r₁ s₂ * s₁)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidOreLocalization.OreSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- OreLocalization.oreDivstatement and proof · cited by 72
- OreLocalization.oreNumstatement · cited by 11
- OreLocalization.oreDenomstatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Localization.mk_mulproof · cited by 12