Theorems · Theorem · commutative algebra
AdicCompletion.AdicCauchySequence.mk_eq_mk
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{m n : ℕ},
m ≤ n → ∀ (f : AdicCompletion.AdicCauchySequence I M), Submodule.Quotient.mk (↑f n) = Submodule.Quotient.mk (↑f m)The defining property of an adic Cauchy sequence unwrapped.
- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 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.
Cites11
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
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.Quotient.mkstatement · cited by 184
- AdicCompletion.AdicCauchySequencestatement and proof · cited by 41
- AdicCompletion.IsAdicCauchystatement · cited by 19
- SModEq.symmproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- AdicCompletion.mk_zero_ofproof · cited by 1
- AdicCompletion.smul_mkproof · cited by 0
- AdicCompletion.map_exactproof · cited by 0