Theorems · Theorem · ring theory
OreLocalization.zero_smul
∀ {R : Type u_1} [inst : Semiring R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {X : Type u_2}
[inst_2 : AddCommMonoid X] [inst_3 : Module R X] (x : OreLocalization S X), 0 • x = 0- Defined in
- Mathlib.RingTheory.OreLocalization.Ring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- zero_smulproof · cited by 716
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.indproof · cited by 18
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