ker_saturated — Mathlib

English

In AddSubgroup, the kernel of any additive group homomorphism is saturated.

Русский

В AddSubgroup ядро любом хомоморфизме идей добавления насыщено.

LaTeX

$$f.ker.Saturated$$

Lean4

theorem ker_saturated {A₁ A₂ : Type*} [AddGroup A₁] [AddMonoid A₂] [NoZeroSMulDivisors ℕ A₂] (f : A₁ →+ A₂) :
    f.ker.Saturated := by
  intro n g hg
  simpa only [f.mem_ker, nsmul_eq_smul, f.map_nsmul, smul_eq_zero] using hg

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