Theorems · Theorem · commutative algebra
Localization.add_mk
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (a : R) (b : ↥M) (c : R) (d : ↥M),
Localization.mk a b + Localization.mk c d = Localization.mk (↑b * c + ↑d * a) (b * d)- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
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.
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- mul_commproof · cited by 2,262
- add_commproof · cited by 1,535
- Localizationstatement · cited by 270
- Localization.mkstatement and proof · cited by 110
- OreLocalization.oreDiv_add_oreDivproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.val_addproof · cited by 4
- Localization.add_mk_selfproof · cited by 0
- Localization.sub_mkproof · cited by 0