isSubDPIdeal_ker — Mathlib

English

For SubDPIdeals J and J', J < J' if and only if J.carrier < J'.carrier.

Русский

Для под dp-идеалов J и J' выполняется J < J' тогда и только тогда, когда J.carrier < J'.carrier.

LaTeX

$$J < J' iff J.carrier < J'.carrier$$

Lean4

/-- The kernel of a divided power morphism from `I` to `J` is a sub-dp-ideal of `I`. -/
theorem isSubDPIdeal_ker {f : A →+* B} (hf : IsDPMorphism hI hJ f) : IsSubDPIdeal hI (RingHom.ker f ⊓ I) :=
  by
  rw [isSubDPIdeal_inf_iff]
  simp only [isDPMorphism_def] at hf
  intro n a b ha hb
  simp only [RingHom.sub_mem_ker_iff, ← hf.2 a ha, ← hf.2 b hb]
  exact congr_arg _

Похожие утверждения