Theorems · Theorem · commutative algebra
LocalizedModule.subsingleton
∀ {R : Type u} [inst : CommSemiring R] {S : Submonoid R} {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
0 ∈ S → Subsingleton (LocalizedModule S M)If S contains 0 then the localization at S is trivial.
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- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- zero_smulproof · cited by 716
- LocalizedModulestatement and proof · cited by 154
- LocalizedModule.mk_eqproof · cited by 15
- LocalizedModule.induction_on₂proof · cited by 5
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