Theorems · Theorem · group theory
Submonoid.LocalizationMap.subsingleton
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoidWithZero N]
(f : S.LocalizationMap N), 0 ∈ S → Subsingleton NIf S contains 0 then the localization at S is trivial.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- MulZeroClass.zero_mulproof · cited by 1,625
- CommMonoidWithZerostatement and proof · cited by 913
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.LocalizationMap.mk'proof · cited by 49
- Submonoid.LocalizationMap.secproof · cited by 26
- Submonoid.LocalizationMap.mk'_secproof · cited by 5
- Submonoid.LocalizationMap.eqproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.subsingleton_iffproof · cited by 2
- IsLocalization.subsingletonproof · cited by 1