Theorems · Theorem · commutative algebra
AdicCompletion.Ideal.mk_eq_mk
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {m n : ℕ},
m ≤ n →
∀ (r : AdicCompletion.AdicCauchySequence I R),
(Ideal.Quotient.mk (I ^ m)) (↑r n) = (Ideal.Quotient.mk (I ^ m)) (↑r m)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.mapproof · cited by 692
- Ideal.Quotient.mkstatement and proof · cited by 610
- Submodule.Quotient.mkproof · cited by 184
- AdicCompletion.AdicCauchySequencestatement and proof · cited by 41
- Submodule.restrictScalars_selfproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.smul_mkproof · cited by 0