commute_map_mul_map_of_isOrtho_of_mem_evenOdd_zero_left

English

Under an isometry setup between Q1 and Qn and Q2 and Qn, the maps map_f1 and map_f2 satisfy a graded commutation relation on evenOdd components.

Русский

При изометрии между Q1,Qn и Q2,Qn отображения map_f1, map_f2 удовлетворяют градуированной коммутативности на компонентах evenOdd.

LaTeX

$$commute_map_mul_map_of_isOrtho_of_mem_evenOdd_zero_left$$

Lean4

theorem commute_map_mul_map_of_isOrtho_of_mem_evenOdd_zero_left {i₂ : ZMod 2} (hm₁ : m₁ ∈ evenOdd Q₁ 0)
    (hm₂ : m₂ ∈ evenOdd Q₂ i₂) : Commute (map f₁ m₁) (map f₂ m₂) :=
  (map_mul_map_of_isOrtho_of_mem_evenOdd _ _ hf _ _ hm₁ hm₂).trans <| by simp

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