prodProdProdComm — Mathlib

English

Applying prodAssoc to ((p1,p2),p3) yields (p1,(p2,p3)).

Русский

Применение prodAssoc к ((p1,p2),p3) даёт (p1,(p2,p3)).

LaTeX

$$$$ prodAssoc\, R\, M_1\, M_2\, M_3 ((p_1, p_2), p_3) = (p_1, (p_2, p_3)). $$$$

Lean4

/-- The product of topological modules is four-way commutative up to continuous linear isomorphism.
This is `LinearEquiv.prodProdProdComm` prodAssoc as a continuous linear equivalence. -/
def prodProdProdComm : ((M₁ × M₂) × M₃ × M₄) ≃L[R] (M₁ × M₃) × M₂ × M₄
    where
  toLinearEquiv := LinearEquiv.prodProdProdComm R M₁ M₂ M₃ M₄
  continuous_toFun := by fun_prop
  continuous_invFun := by fun_prop

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