sum — Mathlib

English

If HasProd f a and HasProd g b, then HasProd (λ x, (f x, g x)) (a b).

Русский

Если HasProd f a и HasProd g b, тогда HasProd (λ x, (f x, g x)) (a b).

LaTeX

$$$\\forall f\\,\\forall a\\,\\forall b, HasProd f a \\land HasProd g b \\Rightarrow HasProd (\\lambda x, (f x, g x)) (a b)$$$

Lean4

@[to_additive]
theorem sum {α β M : Type*} [CommMonoid M] [TopologicalSpace M] [ContinuousMul M] (f : α ⊕ β → M)
    (h₁ : Multipliable (f ∘ Sum.inl)) (h₂ : Multipliable (f ∘ Sum.inr)) : Multipliable f :=
  ⟨_, .sum h₁.hasProd h₂.hasProd⟩

Похожие утверждения