of_symm_smul — Mathlib

English

The inverse map commutes with the smul operation on HahnSeries and HahnModule, i.e., (of R).symm (r • x) = r • (of R).symm x for SMulZeroClass context.

Русский

Обратное отображение commuting с умножением на скаляр: (of R).symm (r • x) = r • (of R).symm x.

LaTeX

$$$((of\,R).symm (r \cdot x)) = r \cdot ((of\,R).symm x)$$$

Lean4

@[simp]
theorem of_symm_smul [SMulZeroClass R V] (r : R) (x : HahnModule Γ R V) : (of R).symm (r • x) = r • (of R).symm x :=
  rfl

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