Theorems · Definition · commutative algebra

AdicCompletion.AdicCauchySequence.mk

{R : Type u_1} →
  [inst : CommRing R] →
    (I : Ideal R) →
      (M : Type u_4) →
        [inst_1 : AddCommGroup M] →
          [inst_2 : Module R M] →
            (f : ℕ → M) → (∀ (n : ℕ), f n ≡ f (n + 1) [SMOD I ^ n • ⊤]) → AdicCompletion.AdicCauchySequence I M

Construct I-adic Cauchy sequence from sequence satisfying the successive Cauchy condition.

Defined in: Mathlib.RingTheory.AdicCompletion.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Cites8

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
Submodulestatement · cited by 7,192
Idealstatement and proof · cited by 4,748
SModEqstatement and proof · cited by 80
AdicCompletion.AdicCauchySequencestatement · cited by 41

Cited by5

Results whose statement or proof uses this declaration.

AdicCompletion.map_surjectiveproof · cited by 2
AdicCompletion.AdicCauchySequence.mk_coestatement and proof · cited by 1
Perfection.teichmullerCauchyproof · cited by 1
AdicCompletion.AdicCauchySequence.mk.congr_simpstatement and proof · cited by 0
AdicCompletion.map_exactproof · cited by 0