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Theorems · Theorem · commutative algebra

Ideal.Quotient.factor_mk

∀ {R : Type u} [inst : Ring R] {S T : Ideal R} [inst_1 : S.IsTwoSided] [inst_2 : T.IsTwoSided] (H : S ≤ T) (x : R),
  (Ideal.Quotient.factor H) ((Ideal.Quotient.mk S) x) = (Ideal.Quotient.mk T) x
Defined in
Mathlib.RingTheory.Ideal.Quotient.Defs
Cited by
1 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingIdeal.IsTwoSidedIdeal.IsTwoSided
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.Quotient.factor_comp_mk · cited by 2Quotient.factor_comp_mkDFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomRing · cited by 7463RingIdeal · cited by 4748IdealHasQuotient.Quotient · cited by 2301HasQuotient.QuotientIdeal.Quotient.mk · cited by 610Quotient.mkIdeal.IsTwoSided · cited by 179Ideal.IsTwoSidedIdeal.Quotient.factor · cited by 33Quotient.factorQuotient.factor_mkCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.