sumSumSumComm — Mathlib

English

The inverse of the sum associativity map is continuous in the homeomorphism setting.

Русский

Обратный к суммасоассоциативности отображается непрерывно.

LaTeX

$$$$ \\mathrm{Continuous}( (\\mathrm{Equiv.sumAssoc}(X,Y,Z) ).^{{-1}} ). $$$$

Lean4

/-- Four-way commutativity of the disjoint union. The name matches `add_add_add_comm`. -/
def sumSumSumComm : (X ⊕ Y) ⊕ W ⊕ Z ≃ₜ (X ⊕ W) ⊕ Y ⊕ Z
    where
  toEquiv := Equiv.sumSumSumComm X Y W Z
  continuous_toFun :=
    by
    have : Continuous (Sum.map (Sum.map (@id X) ⇑(Homeomorph.sumComm Y W)) (@id Z)) := by fun_prop
    fun_prop
  continuous_invFun :=
    by
    have : Continuous (Sum.map (Sum.map (@id X) (Homeomorph.sumComm Y W).symm) (@id Z)) := by fun_prop
    fun_prop

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