Theorems · Theorem · ring theory
OreLocalization.oreDiv_mul_char
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] (r₁ r₂ : R) (s₁ s₂ : ↥S)
(r' : R) (s' : ↥S), ↑s' * r₁ = r' * ↑s₂ → r₁ /ₒ s₁ * (r₂ /ₒ s₂) = r' * r₂ /ₒ (s' * s₁)A characterization lemma for the multiplication on the Ore localization, allowing for a choice of Ore numerator and Ore denominator.
- Cited by
- 8 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.
Cites5
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 · cited by 72
Cited by8
Results whose statement or proof uses this declaration.
- OreLocalization.oreDiv_powproof · cited by 1
- OreLocalization.mul_cancelproof · cited by 1
- OreLocalization.mul_invproof · cited by 1
- OreLocalization.oreDiv_mul_oreDiv_commproof · cited by 0
- OreLocalization.one_div_mulproof · cited by 0
- OreLocalization.mul_cancel'proof · cited by 0
- OreLocalization.mul_div_oneproof · cited by 0
- OreLocalization.mul_oneproof · cited by 0