Theorems · Theorem · commutative algebra
IsHausdorff.haus
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M],
IsHausdorff I M → ∀ (x : M), (∀ (n : ℕ), x ≡ 0 [SMOD I ^ n • ⊤]) → x = 0- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 72 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.
Cites9
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 · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- SModEqstatement · cited by 80
- IsHausdorffstatement and proof · cited by 37
- IsHausdorff.haus'proof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- IsHausdorff.subsingletonproof · cited by 3
- AdicCompletion.of_injective_iffproof · cited by 2
- isHausdorff_iffproof · cited by 1
- IsAdicComplete.le_jacobson_botproof · cited by 1
- IsHausdorff.of_mapproof · cited by 0
- IsHausdorff.iInf_pow_smulproof · cited by 0