Theorems · Theorem · ring theory
OreLocalization.neg_add_cancel
∀ {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] (x : OreLocalization S X), -x + x = 0- Defined in
- Mathlib.RingTheory.OreLocalization.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
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Cites12
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
- neg_add_cancelproof · cited by 256
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.indproof · cited by 18
- OreLocalization.zero_oreDivproof · cited by 8
- OreLocalization.add_oreDivproof · cited by 4
- OreLocalization.neg_defproof · cited by 3
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