add_prod_add — Mathlib

English

As above, equality with product maps is determined by the equality of its coordinate projections.

Русский

Как и раньше, равенство отображения в произведение определяется равенством координатных проекций.

LaTeX

$$$f = g.\text{prod} h \iff (\text{fst}.\circ f) = g \land (\text{snd}.\circ f) = h$$$

Lean4

theorem add_prod_add [ContinuousAdd M₂] [ContinuousAdd M₃] (f₁ f₂ : ContinuousMultilinearMap R M₁ M₂)
    (g₁ g₂ : ContinuousMultilinearMap R M₁ M₃) : (f₁ + f₂).prod (g₁ + g₂) = f₁.prod g₁ + f₂.prod g₂ :=
  rfl

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