leftDistribClass — Mathlib

English

Pull back a LeftDistribClass structure along an injective map; the induced left distribution holds via the injection.

Русский

Предъявляем структуру LeftDistribClass по инъекции; индуцированное лево-распределение сохраняется через инъекцию.

LaTeX

$$Left distributivity on S is preserved: $f(x\cdot(y+z)) = f(xy) + f(xz)$ for all suitable x,y,z.$$

Lean4

/-- Pullback a `LeftDistribClass` instance along an injective function. -/
theorem leftDistribClass [Mul R] [Add R] [LeftDistribClass R] (add : ∀ x y, f (x + y) = f x + f y)
    (mul : ∀ x y, f (x * y) = f x * f y) : LeftDistribClass S where
  left_distrib x y z := hf <| by simp only [*, left_distrib]

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