image_castLE_Iio — Mathlib

English

Let i ∈ Fin(m) and h with m ≤ n. Then the image of Iio i under castLE h equals Iio (castLE h i).

Русский

Пусть i ∈ Fin(m) и h с m ≤ n. Тогда образ открытого нижнего интервала Iio(i) под castLE(h) равен Iio(castLE(h)i).

LaTeX

$$$castLE(h) '' Iio i = Iio (castLE(h) i)$$$

Lean4

@[simp]
theorem image_castLE_Iio (i : Fin m) (h : m ≤ n) : castLE h '' Iio i = Iio (castLE h i) :=
  val_injective.image_injective <| by simp [image_image]

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