associated_comp — Mathlib

English

associatedHom S Q is symmetric in its two arguments: its value does not depend on the order of x,y.

Русский

associatedHom S Q симметрично по аргументам: значение не зависит от порядка x,y.

LaTeX

$$$ associatedHom S Q x y = associatedHom S Q y x $$$

Lean4

@[simp]
theorem associated_comp {N' : Type*} [AddCommGroup N'] [Module R N'] (f : N' →ₗ[R] M) :
    associatedHom S (Q.comp f) = (associatedHom S Q).compl₁₂ f f :=
  by
  ext
  simp only [associated_apply, comp_apply, map_add, LinearMap.compl₁₂_apply]

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