Theorems · Theorem · ring theory
OreLocalization.add_comm
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {X : Type u_2}
[inst_2 : AddCommMonoid X] [inst_3 : DistribMulAction R X] (x y : OreLocalization S X), x + y = y + x- 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.
- AddCommMonoidstatement and proof · cited by 12,281
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- add_commproof · cited by 1,535
- MulActionproof · cited by 1,294
- DistribMulActionstatement and proof · cited by 584
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.indproof · cited by 18
- OreLocalization.oreDivAddChar'proof · cited by 4
- OreLocalization.oreDiv_add_char'proof · cited by 2
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