Theorems · Theorem · commutative algebra

Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality

∀ {R : Type u_1} {M : Type u_3} {M₂ : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup M₂]
  [inst_3 : Module R M] [inst_4 : Module R M₂] (r : R) (rs : List R) (f : M →ₗ[R] M₂),
  ↑(Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner M₂ r rs) ∘ₗ
      (Ideal.ofList (r :: rs) • ⊤).mapQ (Ideal.ofList (r :: rs) • ⊤) f ⋯ =
    (Ideal.ofList rs • ⊤).mapQ (Ideal.ofList rs • ⊤) ((QuotSMulTop.map r) f) ⋯ ∘ₗ
      ↑(Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner M r rs)

Defined in

Mathlib.RingTheory.Regular.RegularSequence

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule