coprod_comp_prodComm — Mathlib

English

Composition on a product commutes with the exchange map: f.coprod g after prodComm equals g.coprod f.

Русский

Композиция на произведении сочетается с преобразованием обмена: $f \circ cok$ равно $g \circ cok$.

LaTeX

$$$f.coprod g \circL ContinuousLinearEquiv.prodComm R M_3 M_2 = g.coprod f$$$

Lean4

/-- Composition of a map on a product with the exchange of the product factors -/
theorem coprod_comp_prodComm [ContinuousAdd M] (f : M₂ →L[R] M) (g : M₃ →L[R] M) :
    f.coprod g ∘L ContinuousLinearEquiv.prodComm R M₃ M₂ = g.coprod f := by ext <;> simp

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