Theorems · Theorem · commutative algebra
Ideal.quotientMulEquivQuotientProd_snd
∀ {R : Type u_2} [inst : CommRing R] (I J : Ideal R) (coprime : IsCoprime I J) (x : R ⧸ I * J),
((I.quotientMulEquivQuotientProd J coprime) x).2 = (Ideal.Quotient.factor ⋯) x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- RingEquivstatement · cited by 1,147
- IsCoprimestatement and proof · cited by 321
- Ideal.Quotient.factorstatement · cited by 33
- Ideal.mul_le_rightstatement · cited by 20
- Ideal.quotientMulEquivQuotientProdstatement · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1