finsetImage_cast_Ioc — Mathlib

English

Let h be a natural equality h: n = m and i,j ∈ Fin n. The image of the half-open interval Ioc(i,j) under Fin.cast h is Ioc(i.cast h, j.cast h).

Русский

Пусть h : n = m и i, j ∈ Fin n. Образ полуинтервала Ioc(i,j) при приведении Fin.cast h равен Ioc(i.cast h, j.cast h).

LaTeX

$$$$ \operatorname{Finset.image}(\operatorname{Fin.cast} h)(\operatorname{Finset.Ioc}(i, j)) = \operatorname{Finset.Ioc}(\operatorname{Fin.cast} h\, i) (\operatorname{Fin.cast} h\, j) $$$$

Lean4

@[simp]
theorem finsetImage_cast_Ioc (h : n = m) (i j : Fin n) : (Ioc i j).image (.cast h) = Ioc (i.cast h) (j.cast h) := by
  simp [← coe_inj]

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