Theorems · Theorem · group theory
Localization.smul_mk
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {R : Type u_4} [inst_1 : SMul R M]
[inst_2 : IsScalarTower R M M] (c : R) (a : M) (b : ↥S), c • Localization.mk a b = Localization.mk (c • a) b- Cited by
- 4 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidSMulIsScalarTower
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsScalarTowerstatement and proof · cited by 3,896
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- one_smulproof · cited by 1,374
- Localizationstatement and proof · cited by 270
- smul_assocproof · cited by 150
- Localization.mkstatement and proof · cited by 110
- OreLocalizationproof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.oreDiv_smul_oreDivproof · cited by 3
- OreLocalization.smul_one_oreDiv_one_smulproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.val_smulproof · cited by 3
- HomogeneousLocalization.awayMapAux_mkproof · cited by 2
- RatFunc.mk_smulproof · cited by 1
- RatFunc.smul_eq_C_smulproof · cited by 0