Theorems · Theorem · commutative algebra
IsHausdorff.subsingleton
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M],
IsHausdorff ⊤ M → Subsingleton M- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- SModEqproof · cited by 80
- IsHausdorffstatement and proof · cited by 37
- eq_of_sub_eq_zeroproof · cited by 27
- Submodule.top_smulproof · cited by 11
- IsHausdorff.hausproof · cited by 6
- Ideal.top_powproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- Polynomial.IsDistinguishedAt.isWeierstrassDivisorAt'proof · cited by 1
- IsAdicComplete.subsingletonproof · cited by 0