English
Pull back a CommGroupWithZero along an injective function; the resulting structure on the domain is a commutative group with zero.
Русский
Переносим CommGroupWithZero вдоль инъекции; домен образуется как коммутативная группа с нулём.
LaTeX
$$$\\text{CommGroupWithZero } M_0' = \\text{ pullback along } f$$$
Lean4
/-- Pull back a `CommGroupWithZero` along an injective function.
See note [reducible non-instances]. -/
protected abbrev commGroupWithZero [Zero G₀'] [Mul G₀'] [One G₀'] [Inv G₀'] [Div G₀'] [Pow G₀' ℕ] [Pow G₀' ℤ]
(f : G₀' → G₀) (hf : Injective f) (zero : f 0 = 0) (one : f 1 = 1) (mul : ∀ x y, f (x * y) = f x * f y)
(inv : ∀ x, f x⁻¹ = (f x)⁻¹) (div : ∀ x y, f (x / y) = f x / f y) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
(zpow : ∀ (x) (n : ℤ), f (x ^ n) = f x ^ n) : CommGroupWithZero G₀' :=
{ hf.groupWithZero f zero one mul inv div npow zpow, hf.commSemigroup f mul with }
