prodSumDistrib — Mathlib

English

A similar distribution on the left: α × (β ⊕ γ) ≃ᵐ (α × β) ⊕ (α × γ).

Русский

Аналогичное распределение слева: α × (β ⊕ γ) ≃ᵐ (α × β) ⊕ (α × γ).

LaTeX

$$$ α \times (β \oplus γ) \simeq^ᵐ (α \times β) \oplus (α \times γ) $$$

Lean4

/-- Products distribute over sums (on the left) as measurable spaces. -/
def prodSumDistrib (α β γ) [MeasurableSpace α] [MeasurableSpace β] [MeasurableSpace γ] :
    α × (β ⊕ γ) ≃ᵐ (α × β) ⊕ (α × γ) :=
  prodComm.trans <| (sumProdDistrib _ _ _).trans <| sumCongr prodComm prodComm

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