Theorems · Theorem · commutative algebra
Ideal.Quotient.factor_comp
∀ {R : Type u} [inst : Ring R] {S T U : Ideal R} [inst_1 : S.IsTwoSided] [inst_2 : T.IsTwoSided] [inst_3 : U.IsTwoSided]
(H1 : S ≤ T) (H2 : T ≤ U), (Ideal.Quotient.factor H2).comp (Ideal.Quotient.factor H1) = Ideal.Quotient.factor ⋯- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- LE.le.transstatement and proof · cited by 3,151
- HasQuotient.Quotientstatement · cited by 2,301
- RingHom.compstatement · cited by 899
- Ideal.Quotient.mkproof · cited by 610
- RingHom.extproof · cited by 331
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.factorstatement · cited by 33
- Ideal.Quotient.ringHom_extproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Quotient.factor_comp_applyproof · cited by 5