rootableBy — Mathlib

English

Any quotient group of a γ-rootable group is γ-rootable; in particular, if A is ℕ-rootable then A/B is ℕ-rootable.

Русский

Любая фактор-группа коректной группы γ-узла является γ-узлом; в частности, если A ℕ-узел, то A/B тоже ℕ-узел.

LaTeX

$$$\text{QuotientGroup.rootableBy}(A, B) : \text{RootableBy } (A/B) \mathbb{N}$ given $[RootableBy A \mathbb{N}]$$$

Lean4

/-- Any quotient group of a rootable group is rootable. -/
@[to_additive /-- Any quotient group of a divisible group is divisible -/
    ]
noncomputable instance rootableBy [RootableBy A ℕ] : RootableBy (A ⧸ B) ℕ :=
  QuotientGroup.mk_surjective.rootableBy _ fun _ _ => rfl

Похожие утверждения