constOfIsEmpty — Mathlib

English

If the index type ι is subsingleton, then the ofSubsingleton map to alternating map equals the corresponding AlternatingMap.

Русский

Если тип индексов ι — подмножественный, то отображение toAlternatingMap от ofSubsingleton совпадает с AlternatingMap.

LaTeX

$$$ (ofSubsingleton R M N i f).toAlternatingMap = AlternatingMap.ofSubsingleton R M N i f $$$

Lean4

/-- The constant map is alternating when `ι` is empty. -/
@[simps! toContinuousMultilinearMap apply]
def constOfIsEmpty [IsEmpty ι] (m : N) : M [⋀^ι]→L[R] N :=
  { AlternatingMap.constOfIsEmpty R M ι m with
    toContinuousMultilinearMap := ContinuousMultilinearMap.constOfIsEmpty R (fun _ => M) m }

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