Theorems · Theorem · commutative algebra
AdicCompletion.of_inj
∀ {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] {a b : M}, (AdicCompletion.of I M) a = (AdicCompletion.of I M) b ↔ a = b- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, 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.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- AdicCompletionstatement · cited by 160
- IsHausdorffstatement and proof · cited by 37
- AdicCompletion.ofstatement · cited by 37
- AdicCompletion.of_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- surjective_of_mkQ_comp_surjectiveproof · cited by 1