Theorems · Theorem · ring theory
OreLocalization.mul_smul
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {X : Type u_2}
[inst_2 : MulAction R X] (x y : OreLocalization S R) (z : OreLocalization S X), (x * y) • z = x • y • z- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- mul_assocproof · cited by 1,667
- MulActionstatement and proof · cited by 1,294
- SemigroupAction.mul_smulproof · cited by 291
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.indproof · cited by 18
- Submonoid.coe_mulproof · cited by 17
- OreLocalization.oreDiv_smul_charproof · cited by 8
- OreLocalization.oreConditionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- OreLocalization.mul_assocproof · cited by 0