finsetImage_natAdd_Ico — Mathlib

English

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

Русский

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

LaTeX

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

Lean4

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

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