Theorems · Theorem · commutative algebra
Localization.add_mk_self
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (a : R) (b : ↥M) (c : R),
Localization.mk a b + Localization.mk c b = Localization.mk (a + c) b- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- Nat.cast_oneproof · cited by 2,501
- Localizationstatement and proof · cited by 270
- Conproof · cited by 152
- Localization.mkstatement and proof · cited by 110
- Localization.mk_eq_mk_iffproof · cited by 9
- Localization.add_mkproof · cited by 4
- Con.symmproof · cited by 4
- Localization.r_eq_r'proof · cited by 3
- Localization.r'proof · cited by 2
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