Theorems · Theorem · group theory
Localization.mk_mul
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} (a c : M) (b d : ↥S),
Localization.mk a b * Localization.mk c d = Localization.mk (a * c) (b * d)- Cited by
- 12 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- OreLocalization.oreDiv_mul_oreDivproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.val_mulproof · cited by 9
- Localization.mk_eq_monoidOf_mk'_applyproof · cited by 4
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- Localization.mk_prodproof · cited by 1
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_memproof · cited by 1
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.smul_memproof · cited by 0
- Algebra.GrothendieckGroup.mk_div_mkproof · cited by 0
- AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjectiveproof · cited by 0
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.primeproof · cited by 0