preimage_castLE_uIoc_castLE — Mathlib

English

Let i, j ∈ Fin(m) and h with m ≤ n. Then the preimage of the interval uIoc(castLE(h i), castLE(h j)) under castLE(h) equals uIoc(i, j).

Русский

Пусть i, j ∈ Fin(m) и h с m ≤ n. Тогда предобраз интервала uIoc(castLE(h i), castLE(h j)) по отображению castLE(h) равен uIoc(i, j).

LaTeX

$$$castLE(h)^{-1}'\mathrm{uIoc}(\mathrm{castLE}(h,i), \mathrm{castLE}(h,j)) = \mathrm{uIoc}(i, j)$$$

Lean4

@[simp]
theorem preimage_castLE_uIoc_castLE (i j : Fin m) (h : m ≤ n) :
    castLE h ⁻¹' uIoc (castLE h i) (castLE h j) = uIoc i j :=
  rfl

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