prodComm — Mathlib

English

Associativity of product diffeomorphisms: ((M × N) × N') is diffeomorphic to M × (N × N').

Русский

Ассоциативность преобразований произведения: ((M × N) × N') эквивалентно (M × (N × N')).

LaTeX

$$$((M \times N) \times N') \cong ((I.prod J).prod J')$-model structure to $M \times (N \times N')$$$

Lean4

/-- `M × N` is diffeomorphic to `N × M`. -/
def prodComm : (M × N) ≃ₘ^n⟮I.prod J, J.prod I⟯ N × M
    where
  contMDiff_toFun := contMDiff_snd.prodMk contMDiff_fst
  contMDiff_invFun := contMDiff_snd.prodMk contMDiff_fst
  toEquiv := Equiv.prodComm M N

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