finsetImage_natAdd_Ioc — Mathlib

English

For any natural m and i, j ∈ Fin n, image of Ioc i j under natAdd m equals Ioc (natAdd m i) (natAdd m j).

Русский

Для любого натурального m и i, j ∈ Fin n образ Ioc i j под natAdd m равен Ioc (natAdd m i) (natAdd m j).

LaTeX

$$$$(\\mathrm{Ioc}\\ i\\ j).\\operatorname{image}(\\mathrm{natAdd}\\ m) = \\mathrm{Ioc}(\\mathrm{natAdd}\\ m\,i, \\mathrm{natAdd}\\ m\,j)$$$$

Lean4

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

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