Theorems · Theorem · ring theory
OreLocalization.subsingleton_iff
∀ {R : Type u_1} [inst : MonoidWithZero R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S],
Subsingleton (OreLocalization S R) ↔ 0 ∈ S- Defined in
- Mathlib.RingTheory.OreLocalization.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- MulZeroClass.mul_zeroproof · cited by 2,091
- MonoidWithZerostatement and proof · cited by 456
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.one_defproof · cited by 10
- OreLocalization.oreDiv_eq_iffproof · cited by 9
- OreLocalization.zero_defproof · cited by 6
- subsingleton_iff_zero_eq_oneproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- OreLocalization.nontrivial_iffproof · cited by 2