Theorems · Theorem · ring theory
OreLocalization.neg_def
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {X : Type u_2}
[inst_2 : AddGroup X] [inst_3 : DistribMulAction R X] (r : X) (s : ↥S), -(r /ₒ s) = -r /ₒ s- Defined in
- Mathlib.RingTheory.OreLocalization.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
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.
- AddGroupstatement and proof · cited by 4,410
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- DistribMulActionstatement and proof · cited by 584
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- OreLocalization.oreDivstatement and proof · cited by 72
Cited by3
Results whose statement or proof uses this declaration.
- Localization.neg_mkproof · cited by 3
- LocalizedModule.mk_negproof · cited by 1
- OreLocalization.neg_add_cancelproof · cited by 0